MIL-HDBU-472mTKE 112 January 1984

TO ALL HOLDERS OF

THE FOLLWINGkGES L!STED:

NEM PAGE

tlttvVflVI!!

ix123

6~1

2. THE FOLLOHING

PAGE

xxlxl!

MILITARY HANDBOOK

MAINTAINABILITY PREDICTION

MIL-HDBK-472 :

PAGES OF MXL-WBK-472 HAVE BEEN REVISED AM) SUPERSEDE THE

DATE SUPERSEDED PAGE MTE

12 Jan 124 my i12 Jan 112 Jari 112 Jan 112 Jan I12 Jan 124 ?kY 1?2 Jan 112 Jan 1

iii 24 my ?966(REPRINTED MITHOUTCHANGE)

v!! 24 *Y 1966V!tf 24 *Y 1966

ix 24 my 1%61 24 MY 1%6

24 hy 1966

(REPRINTED kCNT CHANGE)4 24 my 1%65-1 24 My 1%6

PAGES ARE TO BE ADDED:

DATE

12 Jan 196412 Jan 198412 Jan 1984

Xt!ixiv5

V-1 thru V-33A-V-1 thru A-V-22B-V-1 thru 8-V-27C-V-1 thru C-V-8D-V-1 thru D-V-9

12 Jan 198412 Jan 198412 Jan 198412 Jan 198412 Jan 198412 Jan 198412 Jan 198412 Jan 1984

3. RETAIN THIS NOTICE AND INSERT BEFORE TABLE OF CONTENTS.

4. Holders of UIL-HD8K-472 will verify that page changes and additfonstndicatwl Iwrcio h8v@ baan ●tcrcd. This mttce WI 11 be retained as ● checksheet. Th{s i ssuanct, together w! th appended pages, ~s a separatePublication. Each notice Is to be retained by stocking points unti 1 theMl 1 I tary Handbook !s cmpletely revfsed or cancel led.

INNTY -79021

.

Cust@ans:Amy - M!mavy - ASAir force- 17

Rtviewacttvtttt$ :Amy -my - EC, 0S, SHA!r force - 11, 13, 14

MIL-HDEUM72MOTICE 1

Preparing activity:Wy - AS

(Project MNm-7902)

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MIL-HDBK-472

Prediction facilitates an early assessment of the maturity of themaintainability design and enables decisions concerning the compatlbllfty of aproposed design with specified requirements Or the choice of betteralternatives.

The maintainability prediction procedures I and III are applicable solely toelectronic systems and equipments. Procedures II and IV can be used for allsystems and equipments. In applying procedure 11 to non-electronic equipmentsthe appropriate task times must be estimated. Procedure V can be used topredict maintainability parameters of avlonlcs, ground and shipboardelectronics at the organizational, Intermediate and depot levels ofmaintenance.

In coocluslon, the use of this handbook facilitates the design, development,and production of equipment and systems requlrtng a high order ofma!ntainabil!ty.

1? Jan 1984

xr&HDBK47a2fJ MAY1966

TABLE OF CONTENTS

Pegs

DWRODUCTION

Tbe Need for MaialalaaMMy RecMcUonDefinition of MILbtalndJlll@BMiC Amumptiom zad MerpretatkmsElements of Mnlntalnabiltty Rediction Tecbxdques-mary

MAINTAINABILITYPREDICTION ~OCEDURES

~OCEDURE I

SECTTON1.0 GENERAL

1.1 Philosophy, Assumptions and lihunmary1.2 AppLkabili&1.3 PointofApplication1.4 Basic Parameters of Measurw1.5 Xnforrnatton Required1.6 Data Beeis1.7 Correlztlon Between Predicted and @erved Values

SECTION 2.0 ANALYTIC FOUNDATION

2.1 Structire of Time Elements in “Fix” of Malfunction2.2 Elemental ActiviUes

2.2. I AsmunptionEI Relating to Elemental Actkltks2.2.2 Major Characteristicsof Elemental Activttles

2.3 Synthesis of Time Distributions2.3.1 Modes for Synthesizing Distritnationa of Ttme2.3.2 Cumulstlve Ttme Dtstritmtions and the Monte Carlo

Method

SECTION 9.0 APPXJCA’170N

3.1 Preliminary Procedure3.2 Steps of tbe Prediction %occdure

11223

1-1

1-1

1-11-21-21-21-21-31-4

1-4

1-41-121-141-141-161-161-17

1-19

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TABLE OF CONTENTS (Continued)

3.2 Step-by-Step procedure for Calculating Task Sample3.3 Step-by-Step Procedure for Performing Task Prediction3.4 Calculation of Maintenance Indices

ADDENDUM A DESIGN CHECK LISTS AND SCORING CRITERIA

CHECK LIST A - SCORING PHYSICAL DESIGN FACTORSCHECK LIST 8 - SCORING DESIGN DICTATES-FACILITIESCHECK LI~? C - SCORING DESIGN DICTATES-MAINTENANCE SKILLS

PROCEDURE IV

SECTION I.O GENERAL

1.1 philosophy, Assumptions and SU~rY1.2 Applicability1.3 Point of Application1.4 Basic Parameters of Measurement1.5 Information Required1.6 Data Basis1.7 Correlation Between Predicted and Observed Values

SECTION 2.0 ANALYTIC FOUNDATION

Genera 1H Theoretical Considerations2.2.1 End Item Identification2.2.2 Operational Function2.2.3 Corrective Maintenance Action Definition2.2.4 Malfunction Detection Analysis2.2.5 Preventive Maintenance Task Time Analysis2.2.6 Corrective Maintenance Task Time Analysis2.2.7 Total Maintenance Task Time Analysis

SEC71ON 3.0 APPLICATION

PROCEDURE V

SECTION 1. GENERAL

1.1 Philosophy and Assumptions1.2 Point of Application1.3 Bas!c Parameters1.4 Information Required1.4.1 Method A1.4.2 Method 3

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A3-33A3-47A3-52

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v-1v-1v-2v-2v-2v-2

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MIL-HDBK-472

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TABLE OF CONTENTS (Continued)

Page

SECTION 2. REFERENCED DOCUNENTS v-3

2-1 Issues of documents

SECTION 3. BASIC DEFINITIONS AND MODELS

3.1 MTTR elements3.2 Basic models3.2.1 l+eantime to repa~r3.2.1.1 Mean repair time for the n“ RI3.2.1.2 Average repair time for the n“ RI3.2.2 Percent isolatlon to a single RI3.2.3 Percent Isolation to a group of RIs.3.3 Hean maintenance manhours per repair (=frepalr)3.3.1 Mean maintenance manhours3.4 Nean ma~ntenance manhours per maintenance action (~/NA)3.5 False alarm rates3.6 Nean maintenance manhours per operating hour (~/ON)3.7 Nean maintenance manhours per fl~ght hour (=/FH)3.8 Naxtmum corrective maintenance t!me for the (0)

percentile (Mma. (0)13.8.1 Approximate ~.~, ($>3.8.2 Accurate k.. (@)

SECTION 4. APPLICATION

4.1 Method A, early prediction procedure4.1.1 Predlct\on requirements definition4.1.2 Replacement concept definition4.1.3 Determlnatton of the prediction parameters4.1.4 General prediction model and submdel selection4.1.s MTTR computation4.1.s.1 Method of computing SC and S,4.1.5. 1.1 Nethod 14.1,5.1.2 Method 24.1.5.2 Computation of A, To’ and Tn’4.1.5.3 Deteradnatlon of MTTR4.2 Nethod B - detailed prediction procedure4.2.1 Prediction requirement def!n~t!on4.2.2 Replacement concept definition4.2.3 Fault detection and Isolatton output Ident!flcatlm4.2,4 FD&I outputs and hardware correlation4.2.5 Prepare maintenance flow diagrams4.2.6 Ttme line analysts4.2.7 RI and FD811output correlation4.2.8 Compute ma!nta!nabllity parameters

v-3

v-3

v-3v-4v-4V-6V-6V-6v-7v-7v-7V-8v-9v-lov-lov-lo

v-loV-11

V-II

V-11V-11V-12V-12V-15V-ISV-18V-18V-19V-19v-21v-22v-22v-22V-23V-24V-26V-31V-32v-33

12 Jan 1984

MIL-HDBK-472

TABLE OF CONTENTS (Continued)

APPENDIX A TIME STANDARDS

APPENDIX B ESTIMATES OF M.,. (0) FOR LOGNORMAL REf’AIRDISTRIBUTIONS

APPENDIX C ACCURATE COMPUTER M-.. (Q) ANALYSIS

APPENDIX D ACCURATE MAN.UALMm., (0) ANALYSIS

BIBLIOGRAPHY

Page

A-V-1

B-V-1

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D-V-1

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12 Jan 19B4

MiL-HDBK-472

-LIST OF ILLUSTRA~IONS

Table

1-1

1.2

1-31-41-5

1-6

1-71-8

1-91-10

1-11

2-1

2-22-32-42-5

3-13-23-3

V-I

A-V-I

A-V-II

B-V-I

Table Heading

List oz Categories and Elemental Activities of ActiveReps’r Time

~it~e~ Di;tri~ution~ for ~o~pletion Times for [lementa~

ActivitiesSynthesis of Time DistributionsParameters of Distributions of Elemental ActivitesProDosed Forma’Distribution

Probablllty of

Malfunction ‘Combining MatrObserved Distr

for Determining the Cumulative Time

Completing Elemental Activity of finalest by Designated Timex for Active Repair Time Synthesisbutions of System Final Test Time and

System Logfstic TimeCombining Matrix for System Down Time SynthesisOccurrence Probability Functions for the Elemental

ActivitiesSystem Readouts

Average Parts failures per Part per 106 Hours by partCategory

Halnterlance T&5k TIRejInterchange TimeElement Times Based on the Nork Factor SystemAn Example of the Use of Element Times for Determining

Interchange Time

Part Class Failure Distribution and Sample SizeTask Prediction, R-7801Maintenance Analysis, R-7801/FpS-20

MTTR Elements for Prediction Procedure V

Elemental Maintenance Actions

Common Maintenance Tasks

60th, 70th and 80th Percentiles of the LognormalDlstributlon for Means and Sigmas from .1 to 2.6

Page

1-13

1-15l-~o

1-24

1-2B1-30

1-321-34

Al-38Al-43

2-25

3-173-233-24

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A-V-2thruA-V-5A-v-6

B-V-:thruB-V-i4

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LIST OF ILLUSTRATIONS

Table Table Heading

B-V-I; 90th, 95th and 99th Percentiles of the Lognorma~Distribution for Means and Sigmas from .1 to 2.6

c-v-I Llstlng for Computer Program to Compute M.,, (0) HhenElemental Maintenance Activities are NormallyDistributed

C-V-II Sample Input/Output Data for M.,., (O) Computer progrm

D-V-I Prediction Example Input DataD-V-II Prediction Example Manual Calculation of Mm,. (0)

(0= 0.90)

Page

B-V-15thruB-V-27

C-V-6c-v-7

D-v-8

D-V-9

L

MIL-HDBK-472

LIST Of ILLUSTRATIONS

Figure Figure Heading Page

‘-2!-3

2-12-22-32-42-52-6

3-13-2

;::3-53-63-73-83-93-10

4-14-24-34-44-5

Mnparison Matrix of Maintainability prediction ProceduresDistribution of Malfunction Active Repair Time for theAN/hsB-4

Di~t~{butlOn of 5ystem Down Time for the AN/ASB 4Distribution of Malfunction Active Repair Time for theAN/ARC-34

Distribution of System Down Time for the AN/ARC-34Di~trjbution of ~a~f~n~tion Active Repair Time for the MD-1Jistributlofi of System OowriTime for the MD-1Structure of Time Elements in “Fix” of MalfunctionDistributions of Times Required to Perform Repair ActionsResultants Synthesized from t., tb and tCProbability of Occurrence of System Logistic Time

Functional Level Diagram of a Typical Communications SystemHorksheet for Final Design Malntainabi]iy Predictionldorksbeet AHorkshee! BNorksheet CMorksheet D

Comparison of Population and Sampling Mean DistributionsSample Size NomographMaintainability Prediction FormMaintenance Analysis Continuation SheetMaintenance Diagram AN/GRT-3hNIFPS-20, Tr&nsmltt!ng SystemAmplifier-Mixer, AM-1347/FPS-20Expanded View, Plate Power SupplyPlate Supply, Block DiagramNomograph - Downtime

Procedural Flow Block DiagramRelated Constraint MatrixEnd Item/Corrective Maintenance Action MatrtxEnd Item/Preventive Maintenance ActIon MatrixEnd Item/Operational Functional Matrix

4

1-51-6

1-71-8~_91-!(J

1-111-181-!31-33

2-132-162-322-332-342-35

3-83-1o3-193-203-213-263-273-283-293-32

4-64-144-154-164-17

t41L-liDaK-472

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LIST OF ILLUSTRATIONS (Continued)

-.

Figure

v-1v-2v-3v-4v-sV-6V-7

v-8v-9v-lo

A-V-1A-V-2A-V-3A-V-4A-V-5A-v-6A-V-7A-v-8A-V-9A_iJ_i~A-v-11A-V-12A-V-13A-V-14A-V-15A-V-16A-V-I7A-V-18A-V-19A-V-20A-V-21A-V-22A-V-23A-V-24A-V-25A-V-26A-V-27

~

RI Data Analysis Sheet -RI Data Analysis Sheet -MTTR Submodels

gure Head ng

AB

Definitions of MTTR Submodels TermsMatrix for correlating FD&I Features uith RisFault Isolation Output and RI Correlation TreeManual Fault Isolation Output and RI Correlation tree

(partial)Sample: Maintenance Flow DiagramExample Time Synthesis AnalysisMaintenance Correlation Matrix format

Standard ScrewsHex or Allen Set ScrewsCapt~ve ScrewsDZUS FastenersTridair FastenerThumbscrewsMachine ScrewsNuts or BoltsRetaining R~ngsDrawhook LatchSpring Clip CatchButterfly LatchATR LatchLift and Turn LatchSlide Lock LatchTerminal Posts ConnectIonsScrew Terminal ConnectionsTermipoint ConnectionsH!rewrap ConnectionTaperpln ConnectionPCB ConnectionsBNC ConnectorsQuick Release Coax ConnectorsFrict!on Locking ConnectorFrtctlon Locking Connector with JackscrewThreadlocklng ConnectorSlide Locking Connector

Page

V-13v-‘t4V-16V-17v-25V-27

\-28V-30V-31V-32

A-V-7A-V-7A-v-8A-v-8A-V-9A-V-9A-V-IOA-V-1OA-V-11A,-fl-l!A-V-12A-V-12A-V-12A-V-13A-V-13A-V-13A-V-14A-V-14A-V-15A-V-15A-V-15A-V-16A-V-16A-V-16A-V-17A-V-17A-V-17

12 Jan 1984

MIL-HDBK-472

figure

A-v-28A-v-29A-V-30A-V-31A-V-32A-V-33A-V-3.4A-V-35A-V-36A-V-37A-V-38A-V-39A-V-40A-V-41A-V-42

c-v-1

L;ST OF ILLUSTRATIONS

Figure Heading

Dip ICSGuided CCASGuided CCAS Hith a Tooltion-GuidedCCASModulesCrimp LugsForm LeadsSolde”ing Terminal postsSoldering PCB ConnectionsResoldering Mitt a Braided WickResoldering Using a VacuumForm Flat Pack LeadsPanels, Doors ana CoversDrawersDisplay Lamps

Resulting Repair Time Distribution for a Sample SystemContaining Four (4) Repair Types with DifferentNormally Distributed Repair Times

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Page

A-V-18A-V-18A-v-18A-’V’-19A-V-19A-V-19A-V-20A-V-20A-V-20A-V-21A-V-21A-V-21A-V-22A-V-22A-V-22

C-V-8

12 Jan 1984 ~iv

M]L-HDBK-4~2

INTRODUCTION

MAINTAINABILITY PREDICTION

THE NEED FOR WINTAINA6!LITY PREDICTION: The wediction of the expectednumber of hours tha: a system Or device will be in an inoperative or “downstate” while it is unde”gc;rg maintenance is of kital importance to the userbecause of the adverse effect that excessive downtime has on mission success.Tnerefcre, once the operational requirements of a system are fixed, it iSimperative that a technique be utilized to predict its maintainability inquantitative terms as early as possible during the design phase. Thisprediction shouid be updated continuously as the design progresses to assure ahigh probability of compliance with specified requirements.

A significant advantage of using a maintainability prediction procedure isthat it highl)ghls for the designer those areas of pwr maintainability whichjustify product improvement, modiflcatlon, or a change of design. Anotheruseful feature of maintainabilityprediction is that it permits the user tomake an early assessment of whether the predicted downtime, the quality,quantity of personnel, tools and test equipment are adequate and consistentwith the needs of system operational requirements.

DEFINITION OF MAINTAINABILITY: MIL-STt)-721cieftnesmaintainability as follows:

“Maintainability: The measure of the ability of anItem k be retained in or restored to specificconditions when maintenance is performed by personnelhaving specified skill levels, using prescribedprocedures and resources at each prescribed level ofmaintenance and repair.”

This definition has fostered the development of many maintainabilityprediction procedures for providing an assessment of system maintainability.Each of these uses various quantitative measures to indicate systemmainta~nabllity. However, all of these measures have a speciftc relationshipto, or constitute some element of the distribution of total system downtime,Hence, if a universal method or technique can be developed to determine the“Total System Downtime Distribution” for any type of system, this wouldfacilitate calculat~ng the measures of maintainability currently In use.

HI1-HDBK-472

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BASIC ASSUWTIONS AND iNTERPRETAT10N5: Each maintainability predictionprocedure inc?uded in this handbook deDends upon the use of recordedreliability and maintainability data and experience which have been obtainedfrom comparable systems and components unoer similar conditions of use andoperation, It is a~so customary to assume the applicability of the “principleof transferability.” This assures that data which accumulate from one systemcan be used to predict the maintainability of a comparable system which isundergoing design, development, or study. This procedure is just~fiable whenthe required degree of commonality between systems can be established.Usually during the early design ohase of the life cycle, consnonalitycan onlybe inferred on a broad bas~s. However, as the design becomes refined, duringiater phases of the life cycle, commonality i~ expendable if a high positivecorrelation is established relating to equipment functions, to maintenancetasktimes, and to levels of maintenance. Although the techniques contained inthis handbook have been proposed and appear to fit certain applications, itshould be borne in mind that they have not truly been tested for generality,for consistency one to another, or for most other criteria dealing with broadapplicab!llty. It should also be borne in mind, though, that experience hasshown that the advantages greatly outweigh the burden of making a prediction.For that ~eason, it ~s not the Durpose of this document to deter furtherresearch or Inquiry.

ELEMENTS OF MAINTAINABILITY PREDICTION TECHNIQUES: Each main’prediction technique utilizes procedures which are specificalsatisfy Its method of application. However, all maintainabil”methods are dependent upon at least two basic parameters:

(a) Failure rates of components at the specific assemblyinterest.

ainabilltyy designed toty prediction

level of

(b) Repair time required at the maintenance level involved.

There are many sources which record the failure rate of parts as a function ofuse and environment. This failure rate, is expressed as the number offailures per unit of time. A typical measure Is “failures per 10C hours.”The ma’joradvantage of us!ng the failure rate in malntafnablity predictioncalculations !s that lt provides an estimate of the relative frequency offailure of those components whfch are utillzed in the des~gn. Sim\larly, therelative frequency of failure of components at other maintainable levels canbe determined by employing standard reliability prediction techniques usingparts failure rates. Failure rates can also be utilized in applicableregression equations for calculating the maintenance actfon time, Another useof the failure rates is to weight the repair times for various categories ofrepair activity, in order to provide an estimate of its contribution, to thetotal maintenance time.

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12 Jan 1984

MIL-HDBK-47224 :NY 1966

Repair times are determined from priorexperience, simulation of repair tasks,or past data secured from similar applications. Most procedure break up the“maintmance action”, which is a more general expression than “repair action”,into a number of basicmaintenance tasks whose time of performance is summed toobtain the total time for the maintenance action.

SUMMARY: It is emphasized that the selection and application of the propermahtatibjlity technique results in many economies measured in terms ofman-hours, materiel, and money. These Savingsare attributable to the factthatmaintalnabil!ty prediction is considered to be a tool for des@n enhancementbecause it provkkm for the early recopdtion and elimination of areas of poormaintainability during the early etages of the design life cycle. Othemlse, areasof poor maintainabili~ would only become apparent during demonstration testingor actualuse, afterwhich time, correction of design defjchnciee would becxmtly and uodd y delay schedules end miseions.

Maintainability prediction, therefore, is a most useful instrument to both manageraod engineer becmse itprovideB for improved system effectiveness and reducesadministratiw end maintenance coots.

.

The comparison matxix, Figuru A, (s included to provide● ummary ofthesignifl-oant8ttrfbutesofeach m ahtafn@tlityprediction procedure included fn this hand-book Additional detailo may he obtained by referrfng to specfftc msintatnabilityprediction procedure of Merest.

3

MIL-HDBK-472

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9

12 Jan 1984

MIL-tiDBK-472

PROCEDURE V

1. GENERAL

This procedure can be used to predict maintainability paranete~S of aviOI’tiCS,ground and shipboard electronics at the organizational, intermediate and depotlevels of maintenance. It can also be auplied to any application environmentand type of equipment including mechanical equi~ment. Time standards are forelectronics only.

1,] philosophy and assumptions. The maintainability Procedures presentedoere permit analyzing the maintainability of electronic eCIUiCNM?tIt/SyStW’tISiwliiding direit d[c~n:dbility Zf d!agno;ticjlisolation/test capabilities,replaceablephysical entmaintenancecomponent fastipulations

a. Fapredicted.

b. On’

c. Ma’procedures.

tefnconstruction,-(a replaceable item (RI) is any of thoseties normally removed and replaced to effect repair at theevel for which the prediction IS being made) Dackaging, andlure rates, in addition, the following assumptions andapply to any predictions made using the procedures given here:

lure rates experienced are all in the same proportion to those

y one failure at a time is considered.

ntenance is performed in accordance with established rna!ntenance

d. Maintenance is performed by maintainers possessing the appropriateskills and training.

e. Only active maintenance time is addressed; administrative andlogistlc delays, and clean-up are excluded.

Two separate methods are presented. Method A is an early prediction methodthat makes use of estimated design data and can be applied nwch earlier thanMethod B In the development of an equipment or system. Method B Is a detailedprediction method that uses actual detailed design data to predictmaintainability parameters.

The application of the procedures presented here permits the user to monitorthe overall system maintainability throughout the design and development ofthat system. The user can identify whether or not the specifiedmaintainability design requirements will be met before the system Iscomplete. Thus, if it appears the maintainab!llty requirements will not bemet, the designers can be informed and the necessary changes can be madebefore they become prohibit~vely expensive.

1.2 Point of application. Both of the prediction methods (Method A is theearly prediction and Method B Is the detailed predictim) of this procedurecan be applied at any equipment or system level, at any level of maintenance,and for any maintenance concept pertinent to avtonics, ground electron~cs, andshipboard electronics. (ldhllethe prediction methods were developed

MIL-HDBK-472

specif~cal:y fo’”electronic equipments and systems, there is nothing inherentin the methods t?ia: shoul~ preVefIt th?fr from being applicable to eiect~o-mecnan’cal or me:nanical equipments or s~stems.)

1.] Basic parameters of measure. Mean time to repair (MTTR) ?S the primarjmaintainability Darameter that can be predicted using this procedure. Theotner maintainability parameters that can be D~edictetjusing tnis procedurearp mailmum ~orre~ti~~ maintenance time at tne o Percentile (M... (Q)),Dercent of fau!ts ‘solatatle to a single replaceable item (I ‘; per:ent ~ffaults isolatable to <N replaceable items (1,,),mean mdintenan:e manhoursper repair (EiFi/repai;), mean maintenance mannours per operating hour(~/0~), mean maintenance manhours per fllght hour (WH/FH), (For detailssee DaragraDh 3.2 )

1.4 Information requireq. These data items must be Drovlded as part of themainta~~ Dredlction if they are not provided from another source. (SeeMIL-STD-756 and MIL-STD-1629.)

1.4.1 Method A. To use Method A the following data are necessary:——.

z. The n[]mhorand contents of either actual or estreplaceable it~~;

b. Tne fa)iu e rates, either predictea or estimatedeach replaceable item.

mated) the pr mary

associate w’th

c. The basic fault isolation test strategy of each replaceable Item.

d. The replacement K!ncept, if fault isolation is to a group ofreplaceable items.

e. The packag!ng philosophy

f. The fault isolation resolution, either estimated or required (I.e., %of faults isolated to one replaceable item or the average replaceable itemgroup size).

1.4.2 Method B. The data necessary to implement Method B are:

rep”

rep’

a. The replacement concept for each replaceable ~tem or group of items.

b. The fault detection and isolation outputs associated with eachaceable item.

c. The failure rate of each replaceable item.

d. The maintenance procedure that is followed to remove and replace eachaceable item.

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MIL-HDBK-472

2. REFERENCED DOCUMENTS

~.1 Issues of documents. The following documents of the issue in effect Onthe date of invitation for btd or request for proDosa~, are references In thisDrocedure for information and guidance.

STANDARDS

Militarv

MIL-STD-721 Definitions of Terms for Reliability andMairttalnability

MIL-STD-756 Rellabiltty Modeling and Prediction

MI1-STD-1629 Procedures for Performing a Failure Mode,Effects and Criticality Andlys!s

(Copies of specfflcatlons, standards, drawings, and publ~cat~ons requiredby contractors in connection with specific procu~ement functions should beobtained from the contracting activity or as directed by the contractingoffice~.)

3. BASIC DEFINITIONS AND MODLLS

3.1 MTTR elements. Corrective maintenance actions conslstof the followingtzlsk$: %epa~at~on, Fa~lltIsolation, fault Correction (further broken downinto Disassembly. InterchamJe, Reassembly, Allgnment, Checkout). The time toperform each of-these tasks-is an elemen~ of PIT”called MTTR elements.

The definitions for these MTTR elements and thethe prediction models are as follohs.

MTTR ELEMENT (Abbrevlatton)

R. Hence the task t~mes are

r abbreviations ●re used in

DEFINITION

Preparation (TB ) Time associated with thosem~ to be performed before fau

can be executed.

Fault Isolatlon (Tr, ) Time associated with thosen~ isolate the fault to the level at uh~ch

fault correction begins.

Disassembly (Tb ) Time associated with gafning access“; to the replaceable item or items

identified during the fault Isolationprocess.

Time associated with the removal andreplacement of a faulty replaceableItem or suspected faulty Item,

Time associated with clostng up theequipment after interchange is performed.

Interchange (T, )fl~

Reassembly (T, )nJ

tasks requiredt Isolation

tasks required to

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MIL-HDflK-472

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TABLE V-I. MTTR Elements for Prediction Procedure V.

T 1 Isolation to I Isolatlon to ! Isolation with Mlblguity TIIsolation to I Group with Group IGroup with Iterative! (Requires Further IlSingle RI I Replacement I Replacement I Isolation) II I ) I

I Secondary ~I I~Preparation 1 Preparation ; Preparation { Preparation I Preparation {I I 1 I I !I I secondarylIsolation I Isolation I Isolation I Isolation I Isolation /I I i i I I1lDisassembly ! Disassembly I Disass@nbly I Disassembly \1 I I I II IlInterchange [ !ntewhange I InterchangeI

I Interchange ~ ;::~;daryI I {.-

1 Correctionpreassembly I Reassembly I Reassembly ~ Reassembly I

1 I I I I1- 1

‘ignment I Alignment I Allgnment I Alignment II I I

~rhecko”t I I 1 !,>. ! Checkout ! Checkout ! Checkout !

iIIIIIIIII1II{

I I I I I II

]Start Up I Start Up [ Start Up I Continue I Stati UP I

v-5 12 Jan 1394

MIL-HDBK-472

3.2.:. 1 Mean repair time for the n ‘ Ill.-

J= number of unique FDLI outputs (refer to Daragraph 4.2.3)

A.l = failure rate of those parts of the n“ RI which would cause then‘“ RI to be called ou; in the j’h FDL? output

R.:= average repair time of the n“ RI when called out in the j“ FD~Ioutput as computed below:

3.2.1.2 Average repair time for the n’” RI.

Mnj = number of steps to perform corrective maintenance when a failureoccurs in the n“ RI and results in the j“ FD&I outputs. Includes allma!ritenance elements – preparation, $so~ation. ~t al This may includeoperations on other Ris called out in the j’” fault isolation result. (e.g.isolation to a group w~th iterative replacement).

T. = Average time to perform the m’b corrective maintenance step forn~ the nt’ RI given the j“ FD&I output-

3.2.2 Percent isolation to a single RI. The model for calculating thepercent Isolation to a s~ngle RI (1,) is:

Ks A,k-l

1, = x 100NJ

Mere. An, = failbre rate of those parts of the n’h RI wh!ch wfauldcausethe n“ RI to be called out in the j“ FD&I output.

A, = failure rate associated with the k’” FD&I output whichresults in Isolatlon to a single RI.

K= number of FD&I outputs which result in isolation tc a singleF/l

12 Jan 1984 V-6

MIL-HDBK-472

3.2.3 Pe*cen! isojation to a grodp of RIs The model for calculating thepercent ‘,solaticnto a group of N or less RIs (I.) !s:

PI h.

xN= p= 1 x 100NJ

Hhere; AO = failure rate associated with the p“ FD&I output whichresults in isolation to N or less RIs.

Ae) = same as for I,

P. number of FD&I outputs which resdlt in IsolatlufitG ~ Or ~essRIs.

Other maintenance parameters that can be predicted using these procedures aredS f01~OU5.

3.3 Mean maintenance manhours per repair (~/repair).—.

N~ ?..MMH.

Filil/Repair. n=lNE 1.n=1

Uhere:

N=

1. =

m. .

quant!tyof RI’s

fai)ure rate of n’” RI

mean maintenance manhours required to repair the n’” RI

3.3.1 Mean maintenance manhours required to repair the n’” RI.

v-.712 Jan 1984

llIL-HDBK-472

J = quantity of FD&I results

1. = failure rate associated with the j’” result for the n“ R]

MMH.. = maintenance mannours requiled to repair the n’- RI given the““ FD&J resultJ

(Replace repair times in the apDropr’ate Method A and Method B procedures withthe maintenance manhcur~ required for each reoair action).

3.4 Mean maintenance manhours per maintenance action (~H/MA).

This is the same as ~/repair except that time spent as a result of sySt.emfailure fal;e alarms must also be fncluded in the maintenance manhours.

Two types of false alarms &i-econsidered:

:) Type 1 false alarm is detected during normal operations but cannot berepeated during the fault ~solatlon process.

2) Type 2 false alarm is detected and isolated to an RI when the RI does nothave an actual fault.

F -n s frequency of occurrence of type 1 false alarms ~/

F2n = frequency of occurrence of type 2 false alarms ~1

~1 expressed as a fraction of the nth RI failure rate

WHO = mean maintenance manhours associated with Type 1 false alarms.

M=. = mean maintenance manhours required to repair the n“ RI

-

12 Jan 1984

v-(!

\ 3 5 False alarm ratesoDeratin9 env~ro~mentt

MIL-WK-472

False alarms are dependent on the system type,maintenance environment, svstem design and fault

detection and isolation implementation. Therefore, a standard set of falsealarm values would be impossible to d@rive. A sample of false alarm ratese~perienced on tw~ 1978 vintage equipmen! are presented for referencepurpo$es.

$YS.TEM/EQJ?fWENT Type 1 (F,.)2’ Type 2 (F2,)~

Heapon Contrcl System

●

●

●

●

●

Radar Subsystem .41 .25

Computer Subsystem .63 .65

Control Subsystem 1.32 .31

Power Subsystem .37 .66

Auxillary Subsystem 1.31 .54

Airborne Radar System

● RF Unit

● Transmitter

● !?ecelver

9 Antenna

● Analog Processor

● Digital processor xl

● Digital processor #2

● Control Unit

● Power & Antenna Servo

NA - Not Available

NA

NA

NA

NA

NA

NA

NA

NA

NA

~1 The ratio of type 1 false alarms to actual~/ The ratto of type 2 false alarms to actual

.44

.31

.12

.08

.07

.65

.50

!00

.33

failuresfailures

12 .hn 1%4

v-9

MIL-IiDBK-472

3.6 Mean maintenance manhours per operating hour (~/OH).

This includes the entire manpower that IS required to maintain a system;corrective maintenance, preventive maintenance, and maintenance caused byfalse alarms.

N N PM

2.’ = ),.expressed in failures per operating hour

F. = frequency of r“ preventive maintenance

m, = mean maintenance manhours to perform r’” preventive maintenance type

PM = quantity of unique preventive maintenance types

N = quantity of RI’s

FIn s frequency of occurrence of type 1 false alarms 4/

F2. . frequency of occurrence of type 2 false alarms ~/

PIMHO= mean maintenance manhours associated with type 1 false alarms

~. = mean ma.lntenance manhours required to repair the nth RI

~1 expressed as a fraction of the n’” RI failure rate.

3.7 Mean maintenance manhours per flight hour (~/FH). This is the same as~/OH where k“’ = X. is expressed in failures per fllght hour.

3.8 Maximum corrective maintenance time for the (0) percentile (M.ba(0)). Two Mma. (0) models are provided. The first yields an~oximate value and requires that system repair times be lognormallydist~!buted. The second gives a more accurate value.

3.8.1 Approximate Mm., (0), Appendfx B contains tables of M_a, (0)values for selected values of system 0, system MTTR (MEAN), and standarddeviation of system repair t:me~ (SIGMA) .- !4TTRmay be predicted using MethodA, and the MTTR models in paragraph 3.2.1 above. SIGMA is usually determined‘mm data on similar equipments. Approximate Mm., (41)values for valuesof 4, MEAN, and SIGMA not covered in Appendix B may be calculated by usingthe following equation:

i’-’o

t4:L-HDBK-472

Mma. ($) = exp [log 14TTR+ OSIGMAJ

Nklhere: SIGMA = r.(log R,,; - [(! logR. ; i NJ

d i=l i=i—

N-1

3.8.2 Accurate ti~,.(@). Append~~C presentsa c~puterlzed means Ofpred{ctlng an accurate M.,, @. AppenciizD presents a manual calcu?atlonmethod for predicting an accurate M.,. (0).

4. APPLICATION. The application of the early and detailed maintainabilityprediction techniques is described in 4.1 and 4.2 respectively.

4.1 Method A - early Predlc~ton procedure. This sectiofiprovides astep-by-step procedure for performing an early prediction of mean tire?torepair. The tasks involved in performing the early prediction are:

a. Define the prediction requirements.

b Define the replacement concept.

c. Determine the prediction parameters.

d. Select the appropriate models.

e. Compute the 14TTR(or other parameters).

Descriptions of each of these tasks are provided In the following subsections.

4.1.1 Prediction requirement definition. Th!s step of the prediction is insome resDects the most imDortant as~ecc since it establishes a common baselineof understanding the pred’tcttonpurpose, approach and scope. During thisstep, the malntalnablllty parameter(s) to be evaluated Is defined, theprediction ground rules are established. and the maintenance level for uhlchthe prediction is being made is defined.

Parameter definition Includes the selection (if required) or the parameter(s)to be evaluated and the establishment of a qualitative and quantitativedefinition of each parameter. If the prediction is being performed incompliance ulth a customer statement of work defining the parameter to beanalyzed, it must be determined if the stated parameter is consistent with anequivalent parameter contained in this methodology. if not, the predictionmooels must be changed accordingly, As part of the parameter evaluation, Itmust be determined uhlch elemental maintenance tasks (e.g., preparation,isolation, etc.) are to be included in the analysis and which are to beexciuoed.

The last aspect of th!s step is to explicitly define the maintenance level forwhich the prediction is being made. If the level is defined in terms of aspecific maintenance organization (e.g., direct support unit, depot, etc.),then the tasks to be performed are readily defined by the maintenanceconceptas described in the following section If the level is deftned by operatinglevel or location {e.g., on-site, flight-line. etc.). then this level must beredefined In terms of the maintenance organization(s) performing maintenanceat the leVe~/10CatiOn.

12 Jan 1984v-~1

MIL-HDBK-472

Replacement concept definition. The maintenance concept must beshed, so that in conjunctionwith a definitionof the prediction

requirements (Daragraph 4.1.1), a basellne is established which defines the

4.1.2estab

prediction to be performed. Hith respect to the maintatnabillty prediction,the primary ouput of the maintenance concept is the definition of how a repairis effected and what the replaceable items are.

As part of this process, a complete set of replaceable items is identified.If the maintenance concept allows for fault isolatlon to a group of !?1sandrepair by group replacement, then the RI groups can be reclassified as RIs ~feach of the groups i’sindependent of other groups.

4.1.3 Determination of the prediction parameters. This step involves:

a. Def\ning theRXs.

b. Determining the failure rate (predicted or est!mated) associated witheach RI.

c. Defining fault lsolat~on test methodology for each RI.

d. Defining the replacement concept.

e. Defining the packaging philosophy.

f. Determining the estimated or required fault Isolation resolution(i.e., X% to 1 RI or average RI group size).

Forms slmllar to those in Figures V-1 and V-2 should be used for the datacollection process. Data is collected on these forms at the level for whichpredictions are performed. For example, If a repair time Is to be computedfor every equipment wlth{n a system, then a seperate data collection formshould be used for each equipment. Data should be tabulatd as follows:

F!rst tabulate al? the primary Rls and their associated failure ratesIn tie respective columns of Figure V-1.

b. Next describe all methods (V) for performing each elemental actlvlty(m) in Figure V-2. (Mote that some maintenance act!ons do not require thatall the maintenance elements be fncluded).

c. Next enter the appropriate number of headings (V.) for eachelemental activity along the top of Flgwe V-1.

d. For each elemental activity, (m,v) synthesize times (T-.) usingtimes, selected in accordance w~th paragraph 4.2.6 and note them In therespective column of figure V-2.

e. Next enter the associated failure rate of each RI for the elementalactivity that It pertains to in f~gure V-1.

-

12 Jan 1984V-12

\

.-)

l:!+>,

I cb.-1

Jan 1984

I I; Tm ; ~m ;

I th\ !4TTRElement (m) ~ V ~ Description of the v Method ; v v I

~--- (I

I

II

I

II

I

1

I

I

I

,

I

I

I

I

I

I

I

I (For additional data, see fi12( of bibliograpl~y.)I

I

iI

I

I

I1 II

(

I

I

(

I

I

1

$

ItI

I

I

—.. . . ---- .—. .- —--- . -_l-

12 Jan 1984

I

FIGURE Y-2. P.1Oata Analvsis Sheet - B

I

o

I

(

~

1I

I

(

I

,

1

1

I

II

~I,

tI

II

I

I

1II

I

.

These completed data sheets provide the bas!s for the early predictiontechnioue. Once they are complete the subnmdels can be applied.

4.1.4 General prediction model and submodel selection.

The general form of the prediction mooel is:

Hhere:

70 = Average Preparation lime

7,, = Average fault Isolation Time

T, = Average Disassembly Time.-1, = Average Interchange Time

1. = Average Reassembly Time

7. = Average Alignment Time

7‘c = Average Checkout ?ime

~~, . Average Startup Time

7. = average time of the m“ element of MTTR.

Variations of the model are limited to deleting the time elements forelemental activity terms that are not necessary to complete certainmaintenance actions.

The selection of submodels Is dependent on the replacement policy imposed.The appropriate $ubmodels for computing the average time for the aboveelemental activities are given in Figures V-3 and V-4,

The sutmdels presented are of a general form and can generally be applied toany e~uipment level (i.e.a systgm, subsystem, equipment, etc.). The onlylimitation being that if SC or S, are computed, the prediction level mustbe consistent with the RI grouping rules presented in paragraph 4.1.5.1.Otherwise, the elemental activity submodels are applied at the lowest leve~for which an MTTR prediction is desired.

4.1.5 MTTR computation. The MTTR is computed at the level al which theaverage number of RIs contained in a fault isolation resul~ (S’) or theaverage number of iterations ‘gquireg to correct a fault (S,) isestablished. For example, if S, or SC can be estimated for each equipmentwithin ? system, the~ ~$e lowe$t ~eve! ~h~~ ~h~ U?Tp can be p~ed~cte~ ~j ~;,~

equipment level. Higher level predictions of MTTR, such as system Ievei MT~R,can be computed by taking a failure rate weighted average of the equipmentMTTRs within the system.

:2 Jan :93{

-

. ..*O L“.W

1-

.“b.-’ .J

.“-1 ●“-T—

-“

,,.-,-“

I -“’-.--11..- bL-.z

,t-<

-’---

I>

.--“ : .------

.-j, >--~

-.. ii .--inG

9--

—

●’-.-’ -“.+- 1

,:1-4- .

s’-,. ,.. .

-.-i ●t-i

..~e“

● ,*’ 8

+CJ.

-“l -“-“’.9’ -’”

- *fl

i41L-)@BK-472

.-.

L

urnerqu~re~toprepare* system for laul! Iso~atIon using the vth

%w -mrthud

th%“ -

t)me rqu!red to Isolatc a fdl using the v mclhod .

ttm~ rqulred 10 pcrlorm d16as$embly urJin& the Y111

Tr) -method

v

th‘1

- bmt rqw~d to Interchmge m! RI using the v methcdv

7A - nmc required m ●lign or cslibrste sin i?l using the wth

methodv

!h‘c\ time required to check a rep$tir USIISC the v method

[h‘ST, - time raqtimdM shrtUPn~vw~mu~m~tlwv method

kP, -~aliurerateofItls~s~oc{stedwiththeVthrnethd of perforrmng preps mlloo

th‘F] - failure mte of flls associated with the v method of performing fault

v i301stion

J Dv- failure rete of Rlstssocimtedwtth the Vti method of petiormtng dlss~eemb}y

Ln - faflure rate of RIstmroclafecf w-M the v ti methcd of performing rets*emblyr

‘1 - failure rate of Ills sa-~atedwl~htheVthme~trodof perforMhIK Interchamev

hA - failure mtc of RIsassociatedwith(heVm me- ofperforming slignmentv

‘c - failure mte of Rlsaseocmled with the V* method of performing checkoutv

tsllure raw of IUSassocmtad with the vth

k STV - melhod d ~tlo) IItlng start-up

‘P

‘rl\’u\’RvI

‘A

‘c

‘ST5C

E,

A

7

‘Dm

TRS

- the number of unique ways to perform preparation

th? number of unlquc wrIys to perform (suit lsolatton

- the number of unique wsyri to perform disassembly

- the number of unique ways m perform reassembly

- the number of unlqus umys to perform Merchsnge

- the number of uniqur ways to perform alignment

- the number of untque weys to perform check-out

- thenumber of untque ways to perform ●wrt-up

- the •vem~e number of M corIt8Mted In ● hull Ieoblkon resull

. the s~rage number of tnbrchs~es rsqulred to correct ● fsull

- the number of untque ●ccweees (A s VD or VR)

- the ●verage number of unique accesses required per fault !sofatlon result

- the (allure rate of We M UtU r~ulre the Sw type of Sccess

- the totAl system failure mte

- the tlMC requl red to dlesssemble the Bth

●ccess

th- the tkme ~utred to rasnemble the a cccesa

Flcuu v-l). ~“

L“- 1-

t41L-Hi)BK-472

Computation of repair times below the level at which S(I or G) is establishedm?y result fr an inaccurate account of repair times. The only exception tothis is jf fault isolation is down to a single RI (<’ = 1) for the entiresystem, equ~pment ...), then the MTTR may be computed at any level sinceambiguities between RIs do not exist. Otherwise, the fcllowing criteria mustbe followed:

!n orde;must bewill becomputerepair

to compute a repair time at a given level, a value for 3 (1 orestablished at that level. After the level at which the repaircomputed has been selected, the appropriate models are selectedtime for each elemental activity at that level with higher Ieveimes being computed using a failure rate weighted average.

G)timesto

Values for $C, ~,, ~, ~~’ or ~~’, where required, shouldas detailed in the following subsections.

4.1.5.1 Method of computing 56 and %. Two methods arecomputing the dverage number of RIs in a fault isolationaverage number of iterations required to correct a fault

be comptited

oresented forrgsult (SC) an~ the(S,), compute S (1

or G) using the specified or design requirements, or compute S (1 or G) byassessing the approximate fault isolation capabilities of the system orequipment.

4.1.5.1.1 Method 1. The first method of computing $, or :6 depends uponhow the fau-tion requirements are specified. In the fault Isolationresolution is specified as follows:

X,% to~ N, RIs

h. RI~ < X2%to ~ Nz RIs

N* RI~ ~ X,% to s N] RIs

and X, + X2 + X, = 100

then,

~=x (N;’ ]+ X2( N1+N; +:) .X, (N2+N3;1 )

1~

If the fault !solation requ~rements are spec~fied as follows:

x,% to: N, RIs

x,x to~ N2 RIs

1002 to:ti, I?ls

Hhere X,% c X22 c 1001

i~ idli ;?i+~

MIL.-HDBK-472

~hpr,

(N,+i \ ( N, + ti, + )

x + (X2-X.)= 2 \ 2 ) ‘(100-%2)( “+:’+’)

]o~

pre~i::p~ L!TTRthe specifiedresulting predeving the spec

u;ing this method of computing ~ is based orIthe assumptionfau”t isolatlon requirements have been (or will be) met,ction is the inherent MTTR that will be realized byfied requirements. This approach is valuable during the

ea-;y stages of equiDment development for purposes of allocation andassessment of the requirements facility. This &ppro&ch should tIotbe usedwhen data is available on the actual fault lsolaticm characteristics.

4.I.5.I.2 Method 2. The second method of computing ~, Or <G Involves an————analysis of the fau~t isolation characteristics of the subjectequipment/system as fJllows:

a. P-epare a simple block diagram depicting the system and how eachmajor function is related (i.e., show functional interfaces).

b. Group the functions (RIs) into “G” RI sets such that:

● an estimate of the fault tsolatlon (number of RIs) can bedetermined for each RI set.

estab

cor th~

● each RI $et is independent of any ~ther

● each RI set established is the smallestished.

For each RI set (g) estimate the average fauaverage number of RIs per fault isolation resu

replacement philosophy in question ~~,,Q if iterative>(6,0 if group replacement).

RI $et.

set that can be

t Isolation resolutiont depending on thereplacement,

d. Compute the average $, or ~, for the system or equipment using afailure rate weighted model.

If the repail times are computed at lower levels, then the overall ~ does nothave to bp computed.

4 1.5.2 Computatj~~Of ~ ~r~___and ~o’, The average ni~rntwr of accessg:. .(disassembles and reassemblies) requi~ed per fault isolation result (A) canbe comDuted as follows’

12 Jdn i98:

MIL-HD8K-472

G

I 1,g-l

and,

Mere:

1

Theone

~q = the average number of accesses required per fault Isolatlon resultIn the g“ RI set, (“G” RI sets established the same uay as wasdone for S)

F 98 = the probability that the a“ acces~ will be required for anyrandom fault Isolation result

AQ = the number of untque accesses in the g“ RI set

A9 - the fa~lure rate of the RIs located In the g“ RI set

1qb = the failure rate of the RIs located in the a“ access locationof the g’” RI set

~@ = average number of RIs per fault lsolatlon result for the g’~ RIset

computation of ~D’ and ~u’ is exactly Ilke the method used for ~ wtthmodification. Each probability !s multiplied by its appropriate

disassembly for reassembly time. The equation for ?D’ or ~,’ 1s:

G

ML-HDBK-472

Nhere:

The same equatfons ~lso hold true for reassembly, (~~ ‘)9

where:

T~w. = the disassembly or reassembly time for the a“ access of the~‘h RI set.

Note here also that if the RIs are grouped Into Just one set instead of Gsets, then all the subscripts “g” will fall-out and the failure rate tieighting,of the g“ RI sets Is not necessary.

4.1,5.3 Determination of ?4TTR. The MTTR can nou be computed by sunning upthe average times computed from each submdel. Thus, the MTTR !s expressed as

MMTTR = I 7.

m-l

,,-, . . . . .

HIL-HDBK-472

If the repair time computed is for a lowertimes are cc+nputedas follows.

)4TTR

MTTR. - mean reps’r time of the b’” lower evel

level then the higher level repair

10 = failure rate of the b“ lower level

B - quantity of lower level breakdowns.

4,2 Method B - Deta!led prediction procedure. Thts section provides a stepby step ~rocedure for performing a deta! led prediction of mean tfme to repair(i4TTR)’.

a.

b.

c.

d.

e.

f.

~

h

Descr

4.2.1

pt

The tasks Involved in performing the prediction are:

Def!ne the prediction requirements.

Define the replacement concept.

Identify the fault detection and Isolation outputs (FIXI outputs).

Correlate the FD&X outputs and hardware features.

Correlate replaceable items and fault detection and isolatfonoutput$.

Prepare a maintenance flow diagram.

Prepare time line analyses.

Compute the maintafnab{llty parameters.

ons of each of the tasks are provided in the followlng subsections.

Prediction requirements def!nltion. This step !S similar to thatrequ!red for an early predtctlon; refer to paragraph 4.1.1.

4,2.2 Replacement concept definition. This step is sim}lar to that requiredfor an early pred~ction; refer to paragraph 4.1.2.

v-2?

MIL-1411BK-472

4.2.3 Fault detection and !solation output identification. Th~s stepinvolves the Identification of all the “outputs” which are used in the faultdetection and isolation process. Normally, the fault detection and isolationprocesses are segregated. However, for purposes of malntalnabilltyprediction, the fault detection methodology is considered as the first step offault isolation and is properly included as part of the Isolation capability.Any time associated ulth fault detection (e.g., mean fault detectton time) isnormall~ excluded from the prediction model, but can be included If desired.

The term fault detection and isolation outputs is defined as thoseindications, symptoms, printouts, readouts, or the results of manualprocedures which separately or in combination, Identify to the maintenancetechnician the procedure to be followed.

FD&I outputs wtll vary \n form, format, c~]exity and duta content fromsystem to system and some uIII be more obvious than others. The maintenanceactions taken in response to these outputs may depend upon the systemmaintenance environment and the system operating CritlCa]ltV. It isimportant, therefore, not only to Identify the FD&I outputs but also to ensurethat the FD&I outputs identified are the ones that wII1 be used In theintended maintenance environment.

Some of the more common generic FD&I outputs are:

a. Indicator or annunciator.

b. Diagnostic or BIT output.

c. Meter readings.

d. C)rcuit breaker and fuse Indicators.

e. Display presentation.

f. Alarms.

9. ~mprope~-system operation.

h. Improper system response.

,. System operating alerts.

,-, a----

“o iDply the oreoiction methodology presented herein, the predictor shouldf!rs~ !dentlfv all primary unique outputs upon which the maintenancetechnician relies to make decisions on the repair methodology (e.g., performadjustment. rer)laceRI, proceed to a different method of fault isolation,etc.). Secondary outputs should then be identified for those cases where theprimary output yielded a result which dld not correct the problem and furtherisolation is reQu’red.

MIL-tiDBK-472

4.2.4 FD&I outputs and hardware correlation. The key to this predictto~procedure, and by far the most demanding of the predictiontasks, iS theestablishment of a correlation between the FD&I outputs (See paragraDh 4.L.7)and the hardware for wnlch the prediction is being made. This step jemands athorough understanding of the system hardware, software, monitoring anddiagnostic capabll~ties, and of the FD&I features Inherent to the system,Ft)&Ifeatures are those hardware and software elements, or comb~nat~onsthereof, which generate or cause to be generated each FO&Ioutput.

‘his task can be accomplished either from the top down or bottom bp. The topdown app~oach ~nvolves a fault tree techniaue where the top of the tree ‘seach unique FD&] output; the next tier identifies the FCXI feature(s) whichcan yield the subject output: and, the bottom tier Identifies the RIs orpartial RIs which upon fa!~ure would be detected or isolated by the subject~%: feature. The bottw up approach involves identification of all thecircuitry in terms of RIs associated with each FD&I feature, and the analystsof how a failure of each RI presents itself in terms of a FD&l output.

Either approach requires the same five steps to be performed:

a. Identify all FD&I features.

b. Ident~fy the circuitry associated with each feature.

c. Identify the fD&I sequencing.

d. Establish the RI failure rate associated with each FD&I featUre.

e. correlate the FDLI features with the FD&I outputs.

FD&I features are those hardware and software elements, or combinationsthereof, which generate or cause to be generated each FD&Ioutput. Typicalfeatures include diagnostic program routines, BIT routines, BITE, performancemonitoring programs. status monitors, and test points.

After the FD&I features are icientlfied,the circuit schematics are analyzed toic!entlfythe components tested or verified by each feature. The outputs ofthis analysis are then translated into a matrix as shown in Figure V-5. Thematrix Identifies, for each FD&I feature, the RIs and canponents which aretested by that feature. Also included in the matrix is an identifier whichdefines the order in which the FD&I features are utillzed during the iSOlatiOnprocess.

12 Jan 1984v-24

UIL-HDBK-472

The matrix is used to identify the failure rate of each RI associated witheach Fl)&Ifeature. The first FD&I feature Is examined and the failure rate ofeach componentassociated with that feature \s entered in the matrix underthat feature. The second feature Is then examined. etc. If a component istested by mre than one feature, the failure rate is assigned to the firstfeature which would result in a positive failure indication. If differenttests of the sane component check different failure nxx!es,then the failurerate Is apportioned to each feature based on the relatjve occurrence of eachfailure mode. The failure rates for the components under each RI in each FD&Ifeature column are sumned together and entered as the failure rate for the RIchecked by that particular feature. This assumes the feature e!ther checks asingle RI or can check multtple RIs by some sequencing scheme. Thosecomponents which are not included under any F(MI features represent failuresnot isolated with the FD&l features. The failure rates of the failures notisolated by the FD&I features are noted In the manual isolation failure ratecolumn of the matrix to complete the accountingof the total equlptnentfailurerate. All manual isolatlon cases must be accounted for,

If those cases where the n“ failure rate ts known to result in several FD&Ioutputs, but the allocated failure rates are not known, the rationale for theassumed allocation of the failure rates shall be stated.

FIGURE V-5. Matrix for correlating FD&I features with RIs.

12 Jan 1984

MIL-HDBK-472

The next step in the correlation process is to associate the FO&Ifeatureswith the FDM outputs. This is accomplished using a fault tree type diagramsuch as the sample shown tn Figures V-6 & V-7. The Top of the tree consistsof all FD&I outputs; the second tier contains the Fil&lfeatures uhlchseparatelyor jointly result in the given FD&I output; and, the bottom tierpresents the RIs associated with each FM feature and the failure rateassociated w!th that feature. The circles are used to assign numbers to allunique FD&I outputs. The triangles identify the order in whfch RIs arereplaced when the replacement concept calls for iterative replacement.

4.2.5 Prepare maintenance flow diagrams. Next a maintenance flow diagram(MFD) is prepared to establish the Rel values for insertion in the!lalntenance Correlat~on Matrix (Figure V-10). The MFD is prepared toillustrate the sequence of maintenance required. The symbols used in the t4FDare:

o StartMi Point (i.e., Failure Occurs and isDetected) or Ending Point

I I

o

0n,j

n

Activity Block. The top of the block indicatesa sDeclfic maintenance activity and the bottomind~cates the time assoc~atedwith that act!vity.This is the only symbol that denotes ttme.

FD&I Outputs. Designates the primary or secondaryuniaue FD&I outmt which defines the subsequentmai~tenance activity to be performed. The-’j”associated with the output is entered in thecircle.

Decision Point. Defines a point In themaintenance flow at which time the maintenancetechnician must make a dectslon on whichsubsequent path to take.

Path Identlfler. Uniquely identifieseach pathby unique RI(n) and FD&I output (j).

Continuation. Designates continuationfromor toanother place In the maintenanceflow diagram.

.

12 Jan 1~4 V-26

-“’=”

mRI hncl.ature

610 A fOr&=●7m nj

Fi~ure V-8

mSEQUENCC 3T15TS

rANTENNAK)s4TIOM ARDRATES QANTENM

Mln ANDROLL RATES

Q●1oA =9,s43

1

FIGURE V-6. Fault Isolatlon outpu t and RI correlation tree.

V-27

3:L.HI)BK-L72

-

mI

1

#J~~~,iJtj-ii011 041A.z.106 A ● 0.204

QQ::~039 041 001A = 4.308 k ● 0.204 A. 0.ss9

1 2 1

01 i 039A. 0.2s4 A. 0.120

m{pf031 Ot 1A*13940 ~.’ 0204 A,62b6

I 2 1

610 03 i

ArOB79 A*077S

2 1

I I

1 J

FIWRE V-J. ?!anual fault isolation ou:put and RI correlation tree (partial) .—.

V.7R

HIL-HD%K-472

\The HFD (as Illustrated in Ffgure V-8) starts on the left side of the figuresas a “Fa\lureOccurs and Is Detected” event. If IsolationIs inherentinfault detection, the neKt Item shown in the MFD is the unique FD&I outouts.If isolation is not Inherent In detection, the next ftem in the MFD is thefault detection output. This would be followed by activity blocks whichdefine the procedure followed to achieve fault isolation. The activttyb)ock(s) is followed by the unique primary FD&l outputs associatedwith themaintenanceactions that have been executed.

followingthe FD&I output symbols are shown the activities required for faultcorrection and repair veriflcat~on.

If a FD&I output results fn non-ambiguousmaintenance(i.e., primary isolationto a s~ngle RI, or group RI replacement),then an “End” symbol will directlyfollow the fault correctionand vertftcatfonacttv~tfes. lfeW&J W?pWresults In an ambiguous result, a verification decisionblock IS shownaftereach verificationactlv~ty (except the last). Any actlvlty (e.g., clean-~p)performedafter a positive verificationdecision Is shown In an activityblock(s) between the decisionblock and the End symbol. Associatedwith eachEnd symbol Is a path identifierwhich un!quely ident!fleseach path by RI andFD&I output. For example, the path associated with the second RI and FD&IOutput #12 would be designated as 2, 12.

Care must be exercised to ensure that all possiblemaintenanceactions thatcould be followed as a result of a FD&I output observationhave been accountedfor, especiallythose that result in Manual Fault Isolat\on.

The R.j values are computed by adding the times assoc~atedwith eachactivity block from the “FailureOccurs and Is Detected”event to the“end” event for the subject (n, j) pair. Note that only the act!vityblockshave t~me associated with them. The time entered in the fndiv~dualactivityblocks fs computed from a time ltne analysis prepared in accordancewithparagraph4.2.6. Elemental times entered in the time Ilne analysis areextractedfrom the following sources In the order given:

a. Actual times eKperlencedon the subject equ!pment.

b. Standard times from Appendix A.

c. Actual times experiencedon slmllar equipment.

d. Other recognizedtime sources.

e. Engineeringjudgement.

In the establishmentof the time line analyses, the number of maintainersmustbe considered, For example, If a given equipment has two techniciansperformingmaintenance,one technicianmay perform disassemblyto ach~eveaccess to the faulty RI while the second techniciansimultaneouslyperformsother work. In thematntenance flow diagram, this would show as a singlemaintenanceactlvlty w!th the associated time being the elapsed clock time.If the parameterof Interestwas ~loii, Instead ofMTTR, then the theentered In the actlvlty block would be the combinedMMH in lieu of the elapsedtime.

V-29 12 Jan 1984

KIL-EDBX=472

-

0.-..

b’Is.

eE-

Jan 19B4

--

141L-HDBK-472

4.2.6 Time line analysis. The estimated times used In the two predictionmethodologiesare synthesizedusing a time line analysismethod. A tlw llneanalyslsconststsof computtngthe total elapsed time of a maintenanceacttonby accountingfor the t~me requiredto performeach step. The procedureforperforminga time line analys~s is as follows:

a.

b.times,

c.ma!nta

d.

Identifyeach task that comprisesthe maintenanceaction,

Determinethe t!me requiredtomaintenancetime standards,time

Determinewhich actions can bener IS available.

perform each task by either actualstudies, or englneer!ng judgement.

done sitnultanewslyif more than one

Determtnethe overall time to perform the maintenanceactionbysmnlng up the times to performeach action.

FigureV-9 is an exampleof how a time is synthesizedfor a simple physicaltask. The time associated with each task !s extractedfrom the tableofmaintenance time standards shown in Table A-V-I In AppendixA.

RI NAME: NODULE (l/R) ELEMENTMAINTENANCEACTION: INTERCHANGE

DESCRIPTIONOF THE ELEMENTALTASKS TIME/ACTION QTY TOTAL TIME

REIWVEQUICK RELEASECOAX 0.04 4 0.16

RENOVESLIDE LOCK CONNECTOR 0.09 1 0.09

RE140VEMODULE 0.09 1 0.09

REPLACE!WDULE 0.11 1 0.11

REPIACESLIDE LOCK CONNECTOR 0.12 1 0.12

REPLACEQUICK RELEASECOAX 0.04 4 0.16

TOTAL TIME 0.73

FIGUREV-9 - EXAMPLETIME SYNTHESISANALYSIS

12 Jan 1984

WL-HDBK-472

4.2.7 RI and FD&I output correlation. The results of the precedingsectionare sunanarizedIn a matrix which shows the relationship annng the RIs forwhich the prediction is be!ng performedand the total set of FD&I outputs.The matrix (Figure V-10) identifies the RIs across the top and the unique FD&IOutputs down the left column. In reference to the math models (refer toparagraph 3.2) the RIs are the “n“ paranwters and the FD&l outputs are the “j”parameters. Each RI column is further divided into three columns:

15 I I 1 1’

FIGURE V-10. Maintenancecorrelation matrtx format.

Under each RI column, enter the failure rate (A.j) of the RI (obtainedfrom the FD&I correlationtree) (see FigureV-6) that is associatedwith eachFD&Ioutput. For each untque output which has only one RI associatedwith It,enter a 1 In the ().jcolumn for that combination. For thoseoutputs whichare associatedwith 2 or more RIs, the Q“, value is determinedby thereplacementconcept. If the replacementconcept 1s group RI replacement,enter under Q.j the number of RIs associatedu~th each output. For example,if three RIs could contribute to the same FD&I output, then a 3 ts entered

-

12 Jan 1984

V-32

MI L-HOBK-472

.—

in the Q., for each of those RIs. If the replacement concept is Iterativereplacement, then Q., \s assigned based on the order of replacement. Thatis, the first RI to be replaced upon recognition of the subject F08J output Isdesignated as Q.j = 1, the second Q.j = 2 and sc forth. In cases ofintegrative replacement, the values for each Q.j Is based on the relativefailure rates of the RIs, with the highest failure rate RI assigned as thefirst replacement item.

4.2.8 Compute maintainability parameters. Once the MFD and MalntmanceCorrelation Matrix have been completed, compute the maintainabilityparameter(s) using the equations in section 3.

.- .-_.

-

MIL-IUNK-472

APPENOIX ATM STAKWD5

10. The ti- standards are tabulated in Table A-V-I. The times tabulated inTable A-V-I have corresponding figures referenced which illustrate uhat eachtime represents. Table A-V-II contains coqosite times of ccxmn maintenanceactions that may occur. Colums two and four of Tab?e A-V-II denote whichtires of Table A-V-I were used to synthesize each actlvlty (letters denoteremval (A) and replaceable (B) tires).

20. Other maintenance tasks can easlIy be synthesized by the following method(for an ex~?e. see Figure v-9, in paragraph 4.2.6).

a. List the actions involved for the maintenance task.

b. Obtain the tiws for each action by using Table A-V-I (tiws that arenot Ilsted should be established either by actual data, time studies, orengineering judgemnt).

c. Compute the tim by sumlng up each ind~vidual time.

-.

>lIL-}ll)BK-~72

TABLE A-V-X. &b

TimestandardNumber Description

1

~

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

FASTENERS

Standard Screws

I!exor Allen ~q3e‘ Screws

, Captive Screws:_ .. !.-.. .

DZUS {U4 LUHUOCK)

Tridair Fasteners

Thumbscrews

Machine Screws

Nuts or Bolts

Retaining Rings

LATCHES

Drawhook

Spring Clip

ButWrfly

ATR (spring loaded,pair)

Lift & Turn

Slide Lock

TERMINALCONNECTIONS

Terminal Posts(per lead)

Screw Terminals

Termipoint

Wirewrap

Taperpin

mental maintenance actions.

1Standard Times

Rem we Replace Interchange(min.) (min.) (min. )

0.16

0.17

0.15

0.08

0.06

0.06

0.21

0.34

NA

0.03

0.04

0.05

0.45

0.03

NA

0.22

0.23

0.22

0.09

0.07

0.26

I 0.43

0.20

/ 0.05

i 0.06

0.08

0.46

0.4-4

0.27

\ O*OZ

‘ 0.03

0.05

0.69

0.04

NA

0.64

0.45

0.30

0.24

0.07

I

I

II

I

0.42

0.60

0.35

0.13

0.12

0.14

0.67

0.78

NA

0.06

0.37

0.10

1.14

0.07

NA

0.68

0.14

Reference \Figure ~

A-~!_ 1

A-Y-2

A-V- 3

A-V-4

A-V- 5

A-V-b

A-V- 7

A-V-H

A-1’- 9

A-V-IO

A-IJ- ] !

A-v- I ~

A-V-13

A-V-14

A-v-. i J

A-V-10

A-V- 17

A-V- Ii{

A-v- 19

A-\l_:f)

I

I

I

12 Jan 1984

L maintenance actions (continued). 1

Stidard Times I~

Remove Replace \ lnterc~ge

I 4

Reference

(min. ) I (min. ) I (min. ) ~ Figure

TIMLE A-V-I. Element;

~

Time IStandardNumber Ik2scription

1

~ TERMINALCONNECTIONS (cont. )

I I

I tI A-V-~)

1%-’(-2 i

I

i A-V-2 1

I A-V-2 1

I

!\I ~-1~-z~

A-V-22

i A-L’-23

iA-’; -2JI

\ A-V-25I

I A-v-2611

,j-~-~?I

i

I

1

I~-\l-’)~

A-\’-2y

,j-’:-~q

‘-”,’-,t 1’2

I f\-\’-3o)I

0.14 io.17 !1

0.14 0.13 perl

PCB a) Discretes

b) Flatpacks

c) DIP [Cs

● 8 pin

21

2’J

23

24

25

26

27

28

29

30

31

32

33

34

35

per lead Iflatpack

0.46 0.52

● 14&16 i ().90 \ 0.86I

II

pin

CONNECTORS ,I I

0.17

(). lg

0.08

NA

0.38

0.26

0.21

0.21

NA

0.11

0.13

0.17

BNC (single pin) ~ 0.07 ~ 0.10

0.07 0.12

0.04 , 0.04

NA ! NA

10.18 ! 0.20

, 0.09 \ 0.17

BNC (multi pin)

Quick Release Coax

Friction bcking

Friction Locking with

I

Ione Jack Screw

Thread Locking

I

I

, Slide Imcking i0.09 { 0.12

I1

!JPLUG lN

MODULES

DIP ICS (intoDIP sockets )

CCAS (without tool)(guided)

I (

III

I,

II

1

● 40 pin

● SO pin , 0.04 ~ 0.07I

CCAS (with tool) I

(guided)

● 40 pm 0.06 0.07I

b 80 pin I 0.09 i 0.08

I 1

I

I( ! I

I

12 Jan 1984A-[l_’)

m!l.-ttDBK-472

TABLE A-V-1. ~lmental mimtenance actions (contiwed).—f w 1

Time

Number

36

37

38

39

40

41

42

43

44

45

46

47

4a

49

50

51

52

53

54

I Stad8td Time

IPLUG INMODULB (cow)

,j CCAS (without tcml); (sot @d@I

i● 40 pin

i ● ao pin

III strip wire

cut wire of sleeving

( Dress Wire withISieevilqg

III

I(

MAI

NA

0.04 0.16

0.09 0.11

1- ‘-

Ii-

“crimp hlgs 1- 1-1

Form Leads (perlead)

Trim Lads (perhad)

Adhesives

Conformal Coating

soldering A) TerminalPosts

B) PCB

Reflow Soldering

Tinning Flatpacka(dipping)

Resoldering A) Braid@Wick

B) SolderSucker

FomtI Fla@ack YJEads(Mechsnkslly)

Clean Su tie

Panels, Doors, &Covers

<I

h-1

10.55 , 0.13

2.20 i 0.23

I

i-

Ii-

i-

I

1-1

I0.04 I 0.03

!

12 Jan 1984 A-v-4

i

I11

NA

0.20

0.20

0.10

0.04

0.21

0.27

0.03

0.03

0.68

2.4S

0.22

0.06

0.25●

0.30

0.16

0.09

0.11

0.29

0.07

ReferencxFigure

A-V-3]

A-v-31

A-V- 32

A-V-33

A-V-34

A-V-35

A-V- 36

A-V-37

A-V-38

A-v- 39

A-v-40-

}tlL-liDBK-Li2

TABLE A-V-I. E1-enLal maintenance actions (continued).

Standard ! I RemweNumber Descri@ioa I (min.)

55

56

57

II

Stmdard Time1

Repiane M&w&m@? Reference(min.) (min.) Figtm

MBCELLANEOUS(cont. )

Drawers (Urge) 0.09

Display Ixuxw 0.10

Threaded Connector ‘Ccnrers 0.11

.-–L ....._..__.

0.10

0.11

0.14

-..-— -.

I

0.19

0.21

!

I

i

i

_l

I

0.25

I

i

I

.- —-- --- 1----

A-V-4 1

k-V-42

{

I

:I

III

.-

NOTE: Oata obtained from RADC-TR-70-89, Maintainability Prediction andOemmstration Techniques

A-V-S 12 Jan 1984

CJ

mL?.--

m s--m“7

--w -“

m

1-a0N

m“m

N-L?

-“

m“mN

G:7

—.

.—1-

C-Jm m

In. .-.m C-J G---

m

G “U

<

E.G

a

-“

..— .—— —..—-—. -— —I I

\

o 1+.1+u r)

-.—

m

I .—..—___ —.-

12 Jan 1984 A-v-b

.

●

●

ST ANOAQO !ica~b%’s

THIS TIME ts~OR ALL sTAh’DARG THREADEo FastenersSUCM AS. SLOTTED HE&O. OI+JLLIPS MEAD, AND ~tLLISTERl+ Ao

THE TIME GIvEN IS THE TIME QEOUIRCD TCI QEMOV’EIStEPL ACE THE FASTENER FROM THE HOLE AND DISENGAGE:OR ENGAGE IT L?Y SEVERAL TwISTING MOTIONS OF THEHAND (A PPROXIMATEL~ S TWISTS I

TOOL ffEQUIUEC) IS STANDARD SCa EWDRIVER (FLAT HEAD.

Pt+t LLIm. OR~Exl

FIGURE A-V- 1. Standard screws.

HEX OR ALLEN SET SCREWS

● THIS TIME IS Fo$? HEX OR ALLEN TYPESET SCREWS

● THE TIME GIVEN IS FOU THC TIME TO ?lGHTEN/OR LOOSEN A HExAGONAL TVC% sET SC f4EWUS?NG AN ALLEN TYPE wRENCH

● TOOLS REOUIREO ARE HEX WRENCHES ORALLEN TVPE wRENCHES

II

FIGURE A-V-2. Hex or Allen set screws.

12 Jan 1984

MIL-HDBK-472

CAPTIVE SC$lEWS

● TH6 IS THC TIME FOfl STANOARDFASrENERSTHAT ARE C14PTl VE TO THE PA NE L/B RACUElTUEV SECURE

● THE TIME GIVEN FOR THIS ACTION INCLUDESTHE TIME TO EF4GAGEKIR DISENGAGE THE FASTENERov A SERIES OF TwIS?t NG MOTIONS WI Tti TblE HANO

● THE TOOL I?EOUIREO IS A ST ANOAfl DSCfl EWORIVER[F MT+IEAD, PHILLIPS OR HEX I

FIGURE A-V-3 . Captive screws.

mDZUS FASTENER

● THIS TIME IS rOR FAsTENERS THAT REOUIRE ONLYA 1/4 TuRf’4 TO ENGAGE OR OISEWGAGE fFASTENEnIS cAPTIVE)

● THE T4ME 61v EN IS THE TIME REQu IREO TO ENGAGEOn DISENGAGE THE FASTENf Fl BY A 1/4 TWIsT Mo.TION OF THE HAND

● TME TOOL REQUla EO IS A ST ANOARO SCREWDRIVERIF LATUEAO, PMILLl~ On HEX)

FIGURE A-V-4 . DZUS fasteners.

12 Jan 1984 A-v-8

MIL-HDBK-472

TRIOAIR FASTENER

c THIS FAST ENE’R Is A QUICK ENGAGING FASTENERTH4T REQUIRES LESS THAN ONE TuRN

9 TM!S. TIME INCLUDES THE TIME NECESSARV TOtZNGAGE/OR DISENGAGE THE FASTE!WER USING ATURN OF TwE wAND

c THE TOCJL REQUIRECI IS AN ALLEN wRENCH

I/’/’

-$3=‘,/> ,,/—.,{’

e/“LJ. -. k’

FIGURE A-V-5 . Tridair fastener.

-.

THUMBSCREWS

● THIS FASTENER IS A THREADED SCREW WITH A HEADTHAT CAN SE GRASPED EASILY BY THE HAND

● THIS T{ME WCLUOES THE TIME NECESSARY TO DISEN -GAGE/OR ENGAGE THE FASTENER BV TURNING IT WITH

W’c’

——

THE HAND

● NO TOOU REQUlaEO —

FIGURE A-V-6. Thumbscrews.

12 Jan 1984

..41 ! . ! 1) !:,’,’-.: -,. . . .

MACHINE SCREWS fWITHNUTl

● THIS FASTENER IS ANV THREACWD ~ASTENER 7HA1

DO ES NOT TAP INTO THE ST QUC~URE. INSTEAD ITE?+ GCtCIES INTO A LOOSE NUT

● THIS TIME INCLUDES THE T)ME TO REMOVE/OR POSITION THE FASTENER ANO NUT ANO TI+E TIMEREQuIRED TO TIGHTEN THE FASTENER

● TOOLs REOU!REO ARE A SC REw DQlv EQ AND A wRENc H

FIGURE A-V-7 . Machine screws.

[

NUTS OR BOLTS

● A?4v FASTENER THAT REQUIRES A WRENCHTO TIGHTEN IT DOWN

● THIS TIME INCLUOES THE TIME NECESSARY TOPOSITtON THE w$7ENCW ANO ENGAGE/OR DISEN.GAGE THE FAST ENEF!

la\

I

FIGURE A-’4-8. Nuts or bolts.

12 Jan 1984 ,1-V- 10

RETAINING RINGS

THIS DEvICE IS A.’ U’” SHAPED PIECE OF METAL THATRETAINS A UN! T/COMpONENT IN POSITION

THE TIME GIvEN INCLUDES THE TIME NECESSAQV TOtINGAGE/OR OISENGAGE THIS FASTENER--—— -—SPECIAL PLIERS ARE REQUIRED TO REMOVE /REpLACETH!S FASTENER b i

;

‘;,2

L“

-1-”

FIGURE A-V-9. Retaining rinlls.

DRAWHOOK U$TCH mi,.”I

Llli● ANY LATCH THAT IS S\ MILAa TO THE ONE

SHOWN I Ill● THE TIME lf’+CLUOES THE TIME TO ENGAGE I

DISENGAGE THE LATCH COMPLETELY

● No TOOLS REQUIRED

&

J

FIGURE A-V-1 O. Drawhook latch.

L-v- 1 1

12 Jan 1984

Sw!tw CLIP cnTcll

t ANY LATCN slMILAn TO Tt4E ONE 51 iOWN

● TIME INcLUDES T14E TIME FJECESSARV 70!IWOfNWE~n DtSEM3NiE THE LATcH COM.PLETFLV

* NO TOOLS nEQUIREO

t4JL-III)NK-472

L 1

FUUKE A-V-11. Spchui clip Utch.

EWTTEnFLV LATC~l—— —● nNv LnTc$4 slMILnn To T14E ONE SIKWJN

● TIME W+CLUTWS THE PtECESShnv TIME To cNGAnE/OR DW~NOAmE THE LnTC\l COMWETELY. Nnn~nL-LV coN$lsTs oF CIFTINQ TI+E lfbl! hNO TUnN)tVG ITme,

● NO TOOLS REOUta EO

I

FIGURE A-V-12. Butterfly latch.

ATR LATCH

● ANY LATCH SIMILAR 70 THE ONE S140WN

. TIME INCLUOES 7*$E TIME Nccessnnv Tn uf4scn Ew/

On SCnEW T$+E Ch*UVEn TNE NIB TO HQOnUEttTQ OIS.lENOfiOE THE SeCUREO UN1l. TME TIME OIVEM !S FOmA ●NR OF ATI! LATCNE$.

● MO TOOLS *l! OUtn ED.

/

/

FICURE A-V-13. ATR latch,

12 Jan 1984 A-V-1 2

●

●

●

LIFT ANO TuRNLAICM

I

ANY LATCH SIMILAR 70 THE ONE S+40WN

TIME INCLUOES T?’(E TIME NE CESSAHV TO LIF 1 THEl+ ANa LE aNO TURN 1? ?0 UNSECURE OR SECURE A

DOOR OfJ PANEL

NO TOOLS REQU!UED

I.

1 1

FIGURE A-V-IL . Lift and turn latch.

SLIOE LOCK LATCH

● ANV LATCH slMILAR 10 THE ONE SHOWN

● THE TIME GIVEN IS THE TIME NE CESSARV TOSLIOE 7HE LOCKING DEvICE TO ENCf+GE)OROISENGAGE THE PANEL

● NO TOOLS REQuIRED

FIGURE A-v-l 5. Slide lock laLch.

TERMINAL Posrs

b aNv TERMINAL connection SIMILAR TO THE ONESSHOWN

● THIS TIME IS THE TIMf REQuIRED TO REMOVE ORREPLAcf A LEAD FROM A TEQMINA( (n~ES No*IN CLUOE sOLDEOING OR oESOLOCRINC)

● NE EOLE NOSE IJLIEt?SAfl E REQUIRED fOR THIS TASK

ino0v

?tIL-HDBK-472

●

●

●

SCREW TEQMINALS

ANY TERMINAL CON NE C710N SIMILAR TO THEONE SHOWN

THE TIME GIvEN IS THE TIME REQuIRED TORf MOVE/OR POSITION THE TERMINAL LUG ANDLOOSE N(OR TIGt+TEfw THE SCREW

A SCk EWCIRl Vk8 IS fiEQul RED

FIGURE A-V- 17. Screw terminal connections.

TERM IPOINT cONNECTIONS

● ANY TERMIANL CONNECTION S! MIMF! TO THEONE SHOWN

● THIS TIME IS THE TIME TO REMOVE THE CLIPWITH A PICK OR TwEEZERS ANO THE TIME TOREPLACE lHticLIP WITHA TERM IPOINT GUN

● TOOU REQUIRED ARE TWEEZERS, OR A PICK,ANDA TERMIPOINT GuN

FIGURE A-V-18. Termipoint connection.

. ,,%1

YIL-HDBli-4i2

\

WIREWRAP

J

1● ANY TERMINAL CO NNEC710N SIMILAR TO THE ONE SHOWN

● THE TIME SGIVEN ARE TO REPLAcE THE WI REWQAPWJITHs WI REWRAP GUN AND TO REMOVE THE Connection WITHAN uNWRAPPING TOOL

● TOOLS REOLJIQEL) ARE A WI REWRAP GUN ANO AN UNWRAP.PING TOOL

,,

FIGURE A-V-19. WireWrap connection.

TAPER PIN

● ANY TERMINAL CONNECTION SIMILAR TO THE ONE SHOWN

● THE TtME GIVEN IS THE TIME REG)u IREO TO UNPLUG MATEOR DEM&TE THE CONNECTOR

/-o

y

● NO TOOL REQUIREO

#

‘,

FIGURE A-V-20. Taperpin connection.

%6—

● ANY TEHMINAL CONNECTED O! RECTLV TOTHE PRf NTEO CIRCUITI?V OF A CIRCUIT CARD

● THE TIME GIVEN IS THE TIME REQUIRED TO REMOVE OR

REpLACE f! LEAD ~NOM THE PCB (NO SOLOER!NG OR RE-SOLDERING TIME)

● THE TOOLS REQUIRED ARE A PICK OR NE EDLENOSE PLIERS

r’

FIGURX A-V-21 , PCB connections.

.- ..-.

E-c cowvEc To$ls

● ANv CONWECIOm THn T wA54 BAVONET LOOKING OEV,CE

● TIMEs GIvEN ARE FO~ MA TIN G/DE MA TlMt2 THE COIW.4ECTORSBV A TwISTING MOTION

● NO TOOLS REQu IREO

HFIGURE A-V-22 . BNC connectors.

QUICK RELEASE COAX Connectors

● ANY COAK CON UECTOR THAT cNcAGE5 OR DISENGAGESBV A PMw On PULL MoTION

● TIMEs GIvEN ARE FOP DC MAT? NGfWA71NC THK CONNECTORS BY A DULLING OR J%ISuf NG h@TIc~N / e

● No TOOLS Rf. QUINLU /

M

e

FIGURE A-V-23. Quick release coax connectors.

FRIc710N LOCKING CONNECTORS

● ANV CON NE CTOQ THAT IS MATED ANO SE CUREOeV THE Ffllc TION OF THE PINS ANO/0= CONNFC70RCASE

● THE TIME GIvEN 1$ THE lfME NE CC SSA~V TO MATEOFI DE MAt E THESE CONNECTOR TYPES

● NO TOOLS RECMJIf!ED

FIGURE A-V-24 . fric~ion locking connector.

12 Jan 1984 A-Y-16

!$III.-I{ I)9K-L-J

FIGURE A-V-?5. Friction locking connector wit~]~ackscrew._— — .—-.

lHQEADLOCKING CONNECTOR

● ANV cONIWECTOQ THAT lSSECIJRED8v AlHUEADED CONNECTOUSMELL

● 1-!S TIME GIVEN 15FOR TME DEMATING/MATINGoF THE cONNECTORAND THE SECURING/UNSECURIF4GOF 11 @V A TuHNINGMOTION

● NO TCIOLSQEQUIRED

FIGURE A-V-26. Threadlocking connector.

K

SLIDE LOCKING CONNEC1O9

● ar.Jw CONtU(CTO!=T-IAT IS sIcIJfJ[l) RV A Ll~DE LOCK

● THF TIME GlVEN15T14f TIME REQul\?fDTOMATE/DEMATETHE cONNEC70FI ANL! ENGAGE/CllSfNGAGF THE SLIDE LOCK

● NO TOOLS RCQUIRED

FIGURE ,1-’:-27. Slide lockin~ connector.——

,1-V-17 12 Jan 1984

@

/

U(P fc$

● THIS INCLUDES ANY DIP IC THAT !5 SECURED INa DIP SOCKET

● THE TIME GIVEN IS THE TIME REQuIRED TO UNDLUG,,.&@

;;> / ‘~OR PLUG lN THE DIP IC

● NO TOOLS REOLMR60

‘===

F1CX?9E A-V-28. m“

GuIDED CCA\

● ANY GuIDED CCA THAT IS lNSERTED/REMOVED BYHAWD

● THE TIME GIVEN !S THE TIME TO PULL OUT ORPUSI-I IN THE CCA

. NU TCKJLS REQUIRED

ylcu~ A-v-29. Guided CCAS.

GuIDED CCAS WITH A TOOL

● THIS TIME IS ~swcl AT ED WITH ANY CCA THATIS w4sEf+7E0/REMOVED wlTH A CARD ExTRAc T.lfuG TOOL

● THIS TIME INCLUDES THE TIME REOUIREO TOF9SITION THE TOOL AND REMOVE/REO@CETUE CCA

● A cARo ExTRAcTING TOOL IS REQUIRED

IFIGURE A-V-30. Guided CCAS with a tool.

&_,., 10

M[l.-Ho HK-472

I

NOt+A2UlDE0 CCAt

. TMIS TIME 1S ASSOCIATED WITH PLUG )Nc Alt DSTHAT AQC NOT GUIOEO

L

ID

● Tl+tb TIME lNc LLloES THE TIMC NC CESSAF4 < ro~{LMOVE/RCPLAcC THE ccA r ROM TnL LUG(

COMNt CTOIl IOOC5 NOT I?UCLLM3E 1 ~ME +064 d ml

FIGURE A-V-31 . Non-~;uided CCAs.

MODULES F:,’—. .9 THIS IS THC TIME ASSOCIATED WfTH REMOVING 0$? POC>I

lIONING A MOOULAR AsSEMBLY 41

● THIS TIMC IS THE TIME Nf?CESSARV 10 REMOVE 7+4[ Mf>(). ‘w&ULE Ofi POSITION IT 4N PLACE

%

%.-. #-./..

/4 .d” ,..- ~--

-----

=&● NO TOOLS RCOUIRECI !

‘4’’”I)

F1(XJREA-V-3?. tl[>dules

\. ‘.,C[<lhll> LIJC,~

?!!!%?.

● TH!s 1s TH[ TIML Assf)c IA7CD WITH 5fc(Jut Nc n If 0t141NAL

LUG TOA WIRE

● $?4[ TIML GIVFN lNCLUO[S 114E lIML 10 WSIII(JN !IffW,lll. IN T,4c L uG AN OCOIMP II

● A (141 M01NG 100( IS RCOUIIJ( 1)

\

o 0

12 Jan 1984

I

?lI&HDBK-472

f

Air/ “

L / ,1FORM LEA12S

(1,

!1(,● TH!S IS THE TIME ASSOCIATED WIT* ~ORMING A

LEAD ON A COM-NENT pFil OR TO CONNECTING1,

1? TO A TERMINAL \/i:\

● THE TIME GIVEN 15 7ME TIME NECEsSAa Y 10 GRXPTHE L@ AD W!TH THE PL)ERS ANO FORM IT

( ~~ \

● NEEDLE NOSE PLIERS ARE REQUla E@

FIGURE A-V-34. Form leak.

/’

SOLDERING TERMINAL POSTS

● THE TIME AS50CJATED wITH SOLDERING A LEADTCA TERMINAL POST

/.5

..-

● THE TIME GIvEN M THE TIME TO HEAT THE TERMINAL

B

-.-_=--

IWST AND APPLY THE SOLDER

● A SOLDERING IRON IS REQuIRED

FIGURE A-V-35 . Soldering terminal posts.

SOLDERING =8 CONNECTIONS

● THE TIME ASSOCIATED WITH SOLDERING A LEAD?0 A PCB ETCHING

● THE TIME GIvEN Is THE TIME TO HEAT THE ETCHING

PAD fiND aPPLY THE SOLDER

● A SOLDERING IRON IS REQuIRED

FIGURE A-V-36 . Soldering PCB connections.

A-V-2(-I

MIL-HDBK-472

RESOLDERING USING ABRAIDEDWICR——— .—— —

● THE TIME ASSOCIATE DVVITH RESOLDERING A CONNECTION USINGA BRAIDED COPPER WICK

● THE TIME C!VEN IS THE TIME TO REHEAT THE SOLDER AND EXTRACT u’IT FROM THE PCB OR TERMINAL USING A BQAIDED COPPER wlc~

● A sOLDER!NC IQON AND BRA IDFO COPPER WICK ARE REQUIRED

4

FIGURE A-V-37 . DeSoldering with a braided wick.

DESOLOERING USING A VACUUM— --— .—— - —

● THE TIME ASSOCIATECI WITH DE5C)LOERK+4G A CONNECTIONU51NG A VACUUM ASSISTED RESOLDERING lPf ON

● THE TIME GIVEN IS TI+E TIME REG)u IREDTo REHEATAND SSLJCK. UP’B THE SOLDER

● A DESOLDECIING IRON IS REQUIF4E0

FIGURE A-V-38 . Resoldering using a vacuum.

FORM FLAT PACK LEAOS

THE TIME ASSOCIATECI WITH FORMING FLAT PACK LEADS USING A.,+@O:i.-

MECHANICALLV OPERATEO OIE.:--

“.THE TIME GIVEN IS THE TIME REQUIRED TO ~SITION THE FLATPACKANO AC TUA7E THE MECHANISM

AM+FCHANICALLV OPERATED DEvICE IS uSED TO 00 THIS m

IFIGURE A-V-39 . Form flat pack leads.

12 Jan 1984

ML-HDBK-472

PANELS. OOORS, AND COVERS

● THE TIME ASSOCIATED WITH OPEN/CLOSING PANELS,DOORS, AND COVERS

● NO TOOG REQuIRED

‘+

FIGURE A-V-40. Panels, doors and covers.

DRAWERS

THE T$ME ASSOCIATED WITH O~NINGtCLOSINGOF DRAWERS THAT ARE ON A TRACK

NO TOOLS aEOUl~ED

I

1

\

1

-JFIGURE A-V-4 1. Drawers.

●

●

DISPLRV LAMPS

THE TIMI? REQuIRED TO REMOVE /aEf%ACE PANELINDICATORS THAT POP IN AND OUT

NO TOOLS REQUIRED

g.a~”

---a/

-

\

w

FIGURE A-V-42. DiePlay lamps.

1? ,L3n lQM

MIL-HDBK-472

APPENDIX B

ESTIMATES OF Me,. ($) FOR LOGNORMALREPAIR DISTRIBUTIONS

10. This appendi~ tmovides estimates of K,, ($) for 109normal”Ydistributed repair times. The estimates for ~m,= ($) are tabulated inTables B-V-I and B-V-II. The %.. (0) values are found by:

a. Selectlng the percentileor 99 percent.

b.the NT’from O

c.wttich0.1 to

d.col umn

Locate the mean repair tR of the equipmentlsystem1 to 2.6 in steps of 0.1.

Locate the corresponding

of interest {*I either 60, 10, 80, 90, 95.

me (MEAN) which most closely approyimate$n question The repair times are ~rovided

repair times standard deviation (SIGMA)s estimated for the subject equipment/system. Values are provided from2.5 in steps ofO.1.

Read the value of K,. (0) under the appropr ate percentile

.-

●

R–\l 1

60thi 70th and 80th percentiles of the Iogrmrnal distributionfor means and si~~as from .1 tc 2.5.

.!

.1

.,

.1

.i● d

.1

.1●I.i.!.1.1.1.1● 4.1.1●I.!.1.1

1*..1.1

.2●2● -.:.2.2J92.202.22.2.2...;.

●L6-.2.2.2202.2.2

.!

.2

.3,4

5. ..6.7.8.9

i .G1 .1102] ●J

I .4i ●5

1.6i .71 .61 .92.02.12.22.32,42.5

.1

.2

.3

.4

.5

.6

.7●0

Q

I :G

1 .1

12

I .3I ,41 .5I .61.7J ●P] .?

2.:2.12022.32 .42.5

!32 PF.JC:!:T

.0673]5

.06J 674,(j&~g$47

. c-●GJ /I.-.C323?3.02 SK’ 6.C23J <2.0208!4.0;E756.C1 7J 45.@i5775.014614.013613.C12755.0119s6.01!330.GIC73>.CIC222.OO!J 721.009286.006889.006526.0061s3.007636.007602

201 Q8.174630.146064.123348.106102.0928S5.082564.0 743G3.0675Q.061965.057245.053212●C)49R7

.0466S4

.044005

.04!S27

.039 5C2

.c3 75?2

.035e55

.03429<

.032654

.031551

.03034.3

.02?228

.02E!?6

~~ p~~~~;;~

.109413

.086984

.0 7L’O 73

.:>:~~

.C50535

.044:!32

.0J9899

.036212

.3332Z?

.030657

.02d575

.026754

.025171

.C23 792

.(322 552

.021454

.02046S

.C19576

.018769

.018030

.017353

.016729

.016153

.0156J9

.015123

.229170

.218639

.196038

.173968

.155384

.140157

.127649

.117259

.loe518

.101071

.094652

.089063

.0)34151

.C 7’S793

.075914

.072424

.C 692 7;

.066406

.063791

.06!394

.059 I 88C5?;51

:L1552@.05J>07.051871

13CI?~CE:i7

.142493

.130081

.I134G6

.! 3L9Q2

.OES ~9L

.081369

.Z?74R3,069236.!-)64Q2.060532.357273.?54290.C51 654.C4920C.047193.C45295.S43565.041985.040536.039201.037966.0365?.0.035753.C34757.033624

.26Qj7

.284966~76636.2601 ti342835.226812.212556.2COO04.166953.i791g3.170501.162738.155757.149446. I 43709.138471.133666.129244.!25156.121364.117s37.1;4546.ll14~”i.iu65eo.I05g66

12 Jan 1984

YIL-l IDBK-47:

TABLE .3-;-1.

60th, 7oth and OOth percentiles of the lo~ncrrnal distributionfor means and sigmas ‘rem

.1 to ?.5 (continued).

I’IEAN

.3

.3

.3

.3

.3

.3

.3

.3

.3.3.3.3.3.3.3.3.3.3.3.3.3,3.3●3.3

.4

.4

.4

.4●4.4.4.4.4.4.4.4.4.4.4.4.4.4●4.4.4.4.4.4.4

SIGRA

●1.2.3

:;.6.7.8.9

1 .0

IiJ .31 .41.5I .61.7J .BJ .92.02.12.22.32.42.5

:4.3

:;.6.7.8.9

1 .0

ljI .3I ●4! .51.61.71.81.92.02.12.22.32.4265

60 F’5?CENT

.308999

.291067

.261946

.232534

.206706

.165022

.167000

.151974

.AJ9342

.128616

.119418

.111455

.104500

.096377

.092948●08810J.083748.079818.076252,073001.070026.067292,064772.062441.060278

.413035

.403256

.379013

.349261,3! 9492.292127.267876.246695.228265.212204.198151●165789.174855.!65128.156428.148606.141539.135125.129279.123930.119017.114490.110305.106424.1028I 6

B-V- 7

70 PDICENT

.337417

.34.3064

.A26258

.305822

.262530

.260952

.241768

.22A94~

.2 i 0236

.197.333

.165964

.175889

.166909

.156860

.151606

.145036

.139058

.133595

.128582

.123965

.119698

.115743

.1!2065

.1OG63S

.105432

.441541

.458339

.4$4249

.437678

.415575

.392076

.369238

.34?936

.328447

.310768

.294770

.280314

.267207

.255297

.244443.234519.225415.217036.209302.202142.195493.169305.183529.178126.j 73061

80 PERCENT

.37401 I

.4! 5832

.427476

.421424

.407261

.390244

.372776

.355961

.J4G2i6,325667.312286.300006a266725~78346.268775.259927.251727244107.237007J?303762241 6E!.218344.~!~E67.207707.202636

.477410

.532433.561473.569971.565313.553272.537551.520326.502814.485669.469222.453624.438923.425113.412158.400008.388609.377905.367841.358367.349435.341001.333027.325475.318315

12 Jan 1984

MIL-H.DBK-L72

f)~tt?, 70th and 80th percentiles of the lognorrr,aldistributionfor means and sigmas from . 1 to 2.5 (continued).

9:> ‘.

,55● -.5~,

● -<

● -.5.5.5.3.5,5

5. ..5

5. ..5.5.5,5.5.5.5

:;.5.5

.6

.6

.6

.6

.6

.6

.6

.5

.6

.6

.6

.6

.6

.2

.6

.6.6.6.6.5.6.6●6.6,5

..:.4

.5

.,

.;

.8

.91.01.11021.31.41 .5!.5I ,71.81.92.92.122~ ●3

2,42.5

.1

.2

.3

.4

.5

.6

.7

.8

.91 .01 .1121 .31 ●41 .51.6I .?1.81 .9~ ●2

2.1222.32 .4~ ●5

.515518

.511835

.495415

.4665!91

.436576,406623.378393.352557.329253.s083’69.289687.272960257’351.244440.232236.22117321}108.201917.193497.185758.178Q2.172023.165904.160215.154913

.617183.617998.604883.562133.554030.52389i.493830.465067.438191.413412.390 ?32.370043.351190.334001.318306.303s49490784a2786g4.26753335Z32.247692.23683 b.239595.222909.215727

~~ ~~~c~:~i

.543941,55~17~

.573439

.5,4557

.547097

.525254

.5G1846

.478493

.45605G

.434920

.415246

.397036

.380223

.364711

.350393

.337159

.324903

.313546

.5029g5

.293149

.28396~

.275383

.267337259763.252677

.645504

.674833

.6g7509

.6FC129

.674565

.656516.634874.611644.5813114.565060.542917.521904.502J07.483536.466152.449895.434694.420471,407153.394667.302946.371928.361556.351778.342541

EC ?~=c~t/T

.579215

.642030

.6ai72c,705714,7]2464.708736.698370.684094.66172C.65G407.632878.615571.598744.582540.567030.552239.538165.X? 4788.512061.500010.488540.477534.46R51.457376.447959

.680304

.748023

.798650

.83 I 664

.849315

.854957

.851 8R9

.842848

.829908

.814561

.797851

.760489

.7Q952.745556.728504.71 i923.695887.660436.665585.651333.S7669.s24576.S12032.600013.588494

—...—..

?!:: -}l:; !;!:-.,:?

TABLE B-l’-I.

50:F,,70:h and 8(’)t!? pprcentil~s of the Iognormal distribution

rut!

.7

.7

.7●7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7

.8

.0

.8

.8

.0.8.8

:;●8.8.8.8.8.6.8●6

::.0.8.8.8.6.8

for means and slpmas from .1 cv 2.5 iCUIIL~iIUeCI).

SIGMA

.1

.2

.3

.4,5.6.7.8.9

1.01.1! .2i .31.41.51.61.71 .81,92.0

.1

.2

.3

.4●5.6.7.8.9

1.01.112I .31.4! .51.61 .?I .8) .92.02.12.22.32.42.5

60 PERCENT

,716373.722570.7JJ344.6953E8.670232,641427.611206.5BI076.5513 (J!.524368.498529.47450s.452267.431717.412740.39521 I.379003.363998.350084.337159.325131.313917,303443

293641.284453

.819263

.826070

.S21 164

.806511

.7s4635

.758026

.726?86

.69052J

.668344

.638985

.610877

.584254

.559210

.535753

.513838

.493391

.474321

.456531

.439924

.424408,409895.39630i.383552.371578.360317

70 PERCENT

.746569

.779571,?97??9.803159.7s7639.784357.765936,744451.7214!6.697872.674502.65I 733.&!9817.608888.589003.570172.552370.535559.519669.5i14704.490550.477170.464S!2.452526.441165

.847385

.883082,906002.916678.916780.908498.894042.875355.853997.831150.807670.784153.761OOI.738477.7I 6737.69513R.675921.656893.638774.&1536.605144.589556.574732.5@Q8.5472C12

60 PERCENT

.781022

.852016,909022.950660.977825.992571.997449.994874,986892.975127.9608! 5.944B?2.927964.910570.893030.875581.858387.841557.825164.809251●793gQ.77894B.764568.750696.73732 I

.881526

.9548211.0164671.064867I .099959I .1229451.1356?11.1399421.1377481 .130Q71.1196811.1065431.0914[31 .O751OII .058066j .0406521 .0231101 .0056?8

.986339

.971336

.954692

.936445

.922625

.907248

.692322

12 Jan 1984

?lIL-t?DBK-A~?

TABLE B-i-l.-

60th, 70th and 80th percentiles of the logncnnal distributionfor means and sigmas from . 1 co 2.5 (continued).

ME/it;

.9

.9,9r

:;.9,?.

●9.53

● -.9.2, ~,

.39c-

.>●9.9.9.9.9.9.9a. .Q

● -

1 .01 .0] .01 .01 .01 .0] .,?

1.01 601.01 .01 .01 ●CI soI J1.01 .01 .01.0I .01.01 ,01.01.0I .0

. - .– . m,-, n

SIGMA

.1

.2

.3

.4

.5

.6

.7.

● 5.9

i .01 .11~

1 .31 .41 .51.6I*71.61.92.02.12.22.32.42.5

i.3

:;.6.7

.6

.91.0i .1121.3I ●4I .51.6!.7

1.81.92.02.1222.32.42.5

60 PERCENT

.919954,928s22,92 ~&? 7.91>629.g972] 7.fj752G0.845L>5.~i 61.33.7S5637.755GZ6.72GG89.07601.6?03E2

.644542

.Qolls

.597C96

.575432

.555065

.535921

.517925

.Solooi

.485072

.47C)CJ6Y

.455925

.442572

1.0205041 .03!0351.0317791.0236701.008139

.986831

.961365

.933162

.903469

.673152

.842916

.813247

.784468

.756787

.730318

.705114

.6811F4

.656507

.637043

.616739

.597526

.579374

.562183

.545?21

.532510

70 PERCENT

.947994

.985773I .!2122501 .027526I .0326421 .0291931.0189Q! .C03651

.984775

.363523

.940S46

.917466

.E93302

.E170S25

.84759)

.825270

.603671

.782856

.762e54

.743673

.725304

.707727

.69091 7

.674843

.659473

1 .048473! .0878931.1172321 .136345J .1456481 .1468791 .1408391.1291741.1132351.094194I .0730261.0505081 .027244i .003692

.980191

.956985

.934249

.912100

.890 6! 5

.869640

.649797,830493.811922,?94071.77632:

80 PEI?CEHT

.9816971.0568741 .! 220341 .1756691.2173111.2474961 .267407~ .27e5381.2024351.2805451.2741351 .264272! 25!6271 .237530I .22 I 64?.i .2 C52E51.188163I .1707331.1531921 .1356881.1163331.10[210I .G6438G1 .0 G78641.051753

1.0821801 .1584301.22=701 L840601.3310841.3674491 .3938?0I .4114291.4213641 .424928f .4232851 .4174711.406375I .3967401 .3831791.368189I .3521701.335441! .3182561.300815I .283274j .265756102483541.231142~02’lt173

--

.1:[ -i{!)f{h-+;:

TABLE B- V-; ,

60ch, 70tt~ and 80th percentiles @f the logrtonnal distributionfor means and sigmas from .1 zo 2.5 (continued)..

1 .1J ,11 ●11 ,1i .11 .1

1 .1

1 ●I

1 .1

I ●1

1 .!

I .1

1.1

J .1

! .1

1 .11 .1} .11.11 .11 .1I .11 .1J .11 .1

1.2I .2i .21 .21210212

E121.21 .21.2I .21.2i .21.2121 ●2121212121212

SIGMA

●J●2.3.4.5.6.7.8.9

1.01.112~ .3I .41.51.61.71.8

;::2,1222.32,42.5

●1.2.3.4.5.6.7.8.9

I .01.1121.31 ●41.51.6I .7J .8

; ::2.12.22.32.42.5

60 PERCENT

1.120953I .1326521.1357561.1303161.117617I .096976i .0757681 .0492821.020649

.990198

.960467

.930212

.90044 I

.8?1437

.843389

.8!6413

.790573

.765892

.742364

.71996?

.698665

.678412

.6591=.6406Q.Q3461

1 Z21326I .2343671 .2391051,2359961 225864I .2097671.1888561.1642671 .1370391 .1OBO761.078124[ .0477S21.017512

,987661.950477.930134.902747.876361.851071.826824.803Q?9.781464.760295.740066.720795

I)-y-j

70 PERCENT

1.14EE591.16960312212731.24JW61.2569211.262914j .259956

1.251572J .2392131.2227771.203613] •]~251~

1.1601411.1369981.113493I .0699341 .066554I .0435221.020961

●998957.97756’6.956624.936747.917343.898tW6

I .2491781 02910091 ,3246221 .34966?1 .36 G?134].3750171.3766651 .3722571.3 Q7461 ●349129I .3322971 .3130331 ,2920001.269748I .24672512232881.! 99717I .1762291 .! 529891.1301211.1077151.0858341.064523j .0433061,023 ?03

60 PERCENT

1,1824031.259642J .329565t .390700I .442159I .463793I .5] 59721,539436I .55514!1.564127I .567420\ ,565963I .560676I .5522501.541346I .5285031 .5141681 .4967111.4624321.465578I ,4463461.430696I .4133561.395828I .378392

13825621.3606091.432231I ●4960451.551181I .5973001.6345241.6633281 .6844181.6986301.7068411.7099131.7086491.7037771.695940I .6656951.673519I .6598151.644922I .6291231.6126521.595703I .578434I .5609?8I .543438

12 Jan 1984

60th, 70th and 80th percentiles of the Iognormal distributionfor means ant sigmas from .! cc 2.5 (continue(i).

I .31 .3i .3] ,:

1 .51 .3I .31 .3Ij.*1 .?1 ,:I ,3; .31 .:i ,3I .31 .31 .31.3I .:1’ ●.II. .-

1 .31 .:

7, .-

1 .41 .41 .41 .41 ●4I .41 .41 ,41 .41 .41.4! .41 ,41 .41 .4I .4I .41 .4] .41.41 .4I .41 .4I .4j ●G

12 Jan 1984

sic!%

.12.3.<.5.5

..I

.8

.9I●C1.11~

I .3I .4J .51.61-

i :61.92 .C2 .~222.32.42.5

.12.3●4.5.6.7.8.9

] .0! .!1W2I .31 .41 .5I .6‘7; :8I .92.02.1222.32.42.5

60 PZi?CEliT

1.521641I .335649i ●J4i959I .3408$01 .333C721.3193531 .30CCS71 2780e9i w2524&I1 .224686i .1954751.IE53471 .1:509710104?161 .974?001.045:711 .0163?6

.S~9259

.9Q455

.936615

.911754

.867B74

.864959

.842988

.821953

I.42I91O1.4367461 .4444171.4451411 .43s4041.4278871.4113941.3907761.3666721 .3404651.312257I 382e551 a25276812224121.1921211.IQ1531 ,1327051.1039231.0759101.0487361.022445

.997058,977>~4

.94SOi 6

.92t.~4~

R-t’-f

70 PERCE’;T

1 .3494451 .392164i .42742;1 .4547EC] ●47426EI*&lgEtf

1.4313261 ●4902G21 .4633 ?s1 .4732 G1 .45E3>51 ●441gc’oi .4224; ::1.4 C: 473I ..3 V3J41 ,:5 G~.L?1 .333GfJ51.30s5161 .2859631.26? 5661.239469:216772i .1945021.1727261.151464

i .4496?21.4931791 ,5296001 .5591421.5811341.5959971.6041871.(3)63171 .6030?9i ,5952771.533585J.5697141.5512901,5318721.5109391 ●4689031.466!06I .4428331.4193!6I .3957441.3722671.349004I .32 C0461 .3034cfi1281315

80 ?ERCCNT

1A82723I .4513951 .5:4JE21 .CO04141.658621i .7985551.750194: *78377Ri .&096181 .528966i •gd{p~o

i .S4!) 520i .S524CGI ,621290I .S46?961 .=9480I ,5?96301.2182711 .8051661 .79@E271 .7755171 .7554G0J .74284i1.725818] .708521

1.4826521 .5 Q045I .~61S9] .7 C40331.7648261.618044106635I71.9013591.931906] .9556501.973!831.9351411.992171I .994899I .9939111.9897481.962895J .s737641 .9 Q794I .950254I .9364511 .g~] ~o

I .9060011 .t!a9 743! .873099

MEAN

i.>1.51 .51 .51.51 .51.51 .51.51 ●51 .51.5J .5I ●5i .51 .5I .51.51.51 .51 ●51.5! .5I .51.5

1 ,61.61.61.61.61.61.61.61.61.61.61.61.61.61.61.61.61.61.61.61.6J .61.61 .61.6

for means and ~irma. frnm -1 tn ~ 5 (rnnt+n,,erl). . . .. . . ... ..--, ,

S I GMA

●1.2.3.4.5.6.7.8.9

1.01 .1121.31 .41.51.61.71.81.92.02.)2.22.32.42.5

●❉.2.3.4*5.6.7.8●9

1.01 ●J12I ●31.41.5I .61.71.81.92.02.1222.32.42.5

60 PERCENT

J .5221431.537697I .546553I .5466611 ●5449951.5355051.5210601,5023941.4802461.455333I .4283!3I .3997731+370221I .3400661.3097261 .27942%J .249417! 2198701.1909211.JQ668J .1351801.108502I .0826QI .0576711.033530

1.&!2346I .6385271.6484261.6521401 .fxs9581.642327J .629606I .6130221 .592=91 .56927)1 ●5435591.5160521.4872401.4575771.4274061.3970431.3667371.336689] .30705912779691.249512l&217551.194743) .1665081.143065

~-!J_c,

70 P5?CENT

i .5498671 .594G32i .~184Ci .66289Y1.6870841.7045171 .7155261.7206001 ●i203J61.7153211.7062591.6937621.678420I .660770;.641291I .Q04001.5984551 .57576?1.5525761.5291101.5055381.4620031.4586191 ●4354781.412651

1.650036I .6947711.7336071 .766 I 631.7922791.8120041,8255711.8333561.835838J .6335601.8270691.8169951.8038241.7880851.7702421.7507101 ,R98561.7079951.6853991 .6=3001.638893i .6153391,5917731.568305I .545025

80 PERCENT

I .5829551 ,66?589I .7376451.607068I .8700571.926090I .9749202.016S472.0511732.0791602.1009722.1171432.1262322.1348002.1373912.1365!62.1326452,1262072 ●11 75852o1071192,0951112,08162!2.0674792.0522832.036404

1.6830441.7630521.838905i .9096421.9745082 .032s 752.0847452.1297342.1680422.1999182.225723224589022606982.2712412.277412237988424791072a2754962J2694312,2612542,2512732.2397622.2269632.2130s72.19S321

12 Jan 1984

?!IL- HD9K-472

TABI.E B-V-I.

60th, 70th and 80:h percentiles of the loRnormal distribution,for means and sl~as from .1 to 2.5 (continued).

rlE&ii sIGnA 60 Pt??CENT

I .7I .71 .71 .71 .71 .71 .7I .71 .7; .7:07! .71. ●?1 .7:* 7!.7J ,71.71.71.71.7i .71.71.7].7

1.81.6f ●61 .8! .51,8

1.81.81.81.61.61.6i ,s1.61 ,81.81 .61.61.81.61.61 .a1.61 ,81.6

.1

.2

.J1

.4

.5

.6,7,8

1::1.1121 ●31 .41.5!.5i .71.81 .92.0‘1Z22.32.42.5

.12.3.4,5.6.7.8

1::i .1121.31.41.51.6] ●1

1.61.92.0

:22,32.42.5

1.722525I .7392581 .750030I .?550461 .7543C”Ii .743462I .7377351 .722746I .704075I .6222921.6572G21.531W9: .6037;CI .574(92i .544s25!.5!4724

1.4843581.4540461.4239661.3942671 .36505?I .33642510308435102811341254553

1.6226841.8399061.8515501 .857tM31.6563591.8539941 .8449391.6316571.8146501,7944341.7715211.7464001.?195241.Q13061.6QI131.6322671 .6U20421.5716731.5413561.5112521046!4?11.4521~91.4233941.3952021.367647

70 FmcCI/T

1.7501851.7954:7i.M5152

i ●S630221 .29s8461.915C)1 .9345a3! .9447s:1.9498501.9501 w1 .94G2@a1 .YZ85G;1 .3275231.9!3795!.ss77161.879-/07j .6&3!3C1 .S3S3031 .817523i. 7950191 .7?200GI .74R6Q1.7251391.7o15&~1 .67S039

1.8503171.8953871.9365131.9715452 .0008B82.0245002 .0424s22.0550532.0 S252S2.0652842.0637552.05838G2.0496302 .037s2 62.0236942.0073221.9691661.969543: ●9487571 .92704!1 .9046?21.681 6;21 .!35S41 6i .8349321.611362

62 PERCENT

1.783121I .e636491 .9395822.0118452.0783292.1389122.1932642J241242Q ~P~g67

;.3182982.3478042.371 7322 .39a4r342.4044392.4; 41652.4290082.422-3772.4216682.4183092.4125802 .4048!02 .3952792.3342332.3718982.35E!4R

I .8531e91 ●9637942.0409132.1137492.1616372.2440682.3006972.5513382.3359502.4346222.4675452 .4s49312.5172922.5348142.5479452.5570752 .5e5932.5646702.5642502.561OE92.5556662.5462692.5391522,5285432.5i 6649

-.

mti

60th, 70th and 80t11percentiles of the lo~normal dist:ibutior,. - . . .. . .- - ..- - - ...- - - - --- . - -- - . . -- - - .-—-

I .91 .9! .91 .91 .9I .9~ ●9

1 .9! .91 .91.9J ●91 .31 .91 .9i .91 .91 .91.91.91 .9i .91 ●9

1 sI .9

2.02.02.02.02.02.02.02.02.02.02.02.02.02.02.02.02.02.02.02 ●02.02.02.02 ●G2.0

SIGf14

.:

.2.3.4.5.6●7.8.9

! .01 .1I .21.3I .4! .51.61 .71.8

; ::2.1222.32.42.5

.1

.2

.3

.4

.5

.6

.7

.8

.91.01.1J.21 ,31.41 ●51.61.71 .B1 ●92.02.1222.32.42.5

60 PERCENT

1.9228261 .9404671 .9528561.9599711.9619371 ●9590041.9515031.9398301.9244231.9057451.8842561.660415I .8346421.807336! .7788541.749516J .719604J .689359I .656968I .fZ?8667I .5985401 .~667271.5393251.5104091.482040

2.0229532.0410062.0540492.0620712.0651752.0635562.0575002.0473392.0334622.01Q761 .99=06J .9736621 .949045I .922731I .895065~ .8663631.8369051 .80s38J .7766751.746304i .7159791.685832! ,6559741.626493I .5974Q

~-f!-: 1

?0 PERCENT

1.950434I .9964932. C377212. G737852.1044852.12975!2.!496402,1643!32.1740212 .I 790832.1798672.1767662.1701662.1605302.148!892.1335322.{ 169052.0986212.0769692.0582022.036550i.0142i Z1.9913=1.968153].944?16

2.0505382.0369452.1386002.1757862.2 U77042.2344642.2560872.2726902.2844712L91052.2946762 029375B2 Z!893032.2 S16782.2712442.2503492.243322202264692.2080732.1883882.1676462.1460522.!2378P2.1010162.077876

80 PERCEti7

! .s8324E2.0640952./a I7252.2154072.2645202.3405762 ,4 C72202,4602372.5075432.549166Z .56%Z362.6159592.6416052.6Q4812.6789262.69i2892 .69992i‘2.7051682.7073622.7066212.7038412.6986972.6916432.6~9J02.6727!C

2.0833012.1643602.2424372.3168612.3 B70522.4525412.5129752.5661202.6178552.6 S21672.7011302.7348982.7636822e?B?7402 .go73632.8228572.8345402.g427292.8477342.8498552.8493782.8465702. R416RI2.8349422,826567

12 Jan 1984

rw N

2,i?*!9’*..2.12,12.1?!L..2.19G.!2. I2.:2012.12.4~7!

2.:~... . 12“.,Q,L*.2.12.iZ.i2.19L.!2.1

?:; i. -Ili)i, f:-..;.

TABLE B-!’-I.

61JthJ 70rh and flOtll percentiles of the lognonnal distributionfor means and sigmas from ,1 to 2.5 (continued).

~]Gm&

.12

,.J.4.5.6.7●8.9

1.01.1102I .31 ●AI .51.6i .7la, .“I .92.02.1222.32.42.5

.1

$.4.5.6.7.89

1 :C1.1! .2J .3I .4I .51.6j .71.61 .92.02.1222,32.42.5

2.1230682,1414792.!5512C2.1U9732.lwl152.1677il2.lf&?9132.154253~*14j9:]

2.1260892.1074972.0661542 ●OQ 7332.0374572.01C 6371 .982730I .9536431 .9242821.894268I .8639S2I .8336191 .8CU3~1.7731271 .7432291.713660

2&!231732.241SC62.256092226570422707992.2715112.26803822606322 .2495B92.2352332.2179952.1979532.17:7192.! 515372.1257212.0 S8~662.0703432.0412982.0116501.9815971.9513081 .9209341.8906031.8604?4I .8304S2

70 PERCEUT

2.! 506332.1373522.23976?2.2775242.3105992.3367~32.3619:72.3802932 .39399s2.4032452.4083052.4094762.4070612.4 C142C2.392S16:.3815032.3664232 .35307C2.336@192.3175212.2978072.2770672.2555472.2333542.21 G65G

2.2507162.2977!92.3406422 .37g2072.4132162 .44255?2.4672092.467216? .5027022.513PA72.5206652.5240292.52361~2.5199322.5132742.5039432.4922342.4?84262.4627e42.4455552.4269662.4072272.3665272.3650352.342909

80 PERCENT

2.1833482 .26459S2.3430672.41 g1442.489288:,5560492.6180792.6751332.7270662 .77392?2.8154492,6520392.8837592 .910E232.9534762.>~!905

2.9666352.977712Z .9 B5X152,9902932.9923462.99! 3262.9892772.9846222.978176

2 .2 S339C2.3648052.4436272.5192652.5912752.6591692.7226282.7814002.e353232.6843162.9283642.9675863.0020493.0319433.0574733.0788723 .09&3883.1102833.1208173.1282533.1328463.1348413.[344733.i319663.127527

12 Jan 1984

q11.-l{!)i\};-4?~

TABLE B-V-;.

60rtI, 70th and 80th percentiles of the lognomal distributionfor means and siQmas from .1 LO 2.5 [continued).

FIEAN

2.32.32.32 .32.32 ●32.32.32.32.32 ●32 ●32 *32.32.32.32.32.32.32.32.32.3~ ●J

2.32.3

2.42.42.42.42.42,42.42.42.42.42.42.42.42.42.42.42.42.42.42.42 ●42.42.42.42,4

SIGMA

.192.3.4.s.6.7.8.9

1.01.11.2J ●3I .41,51.61.71.81.92.02*1229b ●52.42.5

.12,3.4.5,6.7.8●9

i ●o

IiI .31,4I .51.6I .71.8

; ::2.1222.3

; ::

60 PD?CENT

2.3232682.3422962.356S782.3672842.3732552.3749992.3726842.3665292.3567922.3437632.3277402.30906322680262J?649472.24012422138392.1863552.1579132,1287332.0990112,0689232 .1338&?42.0082491.9779151,947724

2.4233552.4426522.4577902.4687342.4755J12,4762102.4769742.4719912.4634912.451?282.4369792.4195332.3996812.3777122.3539062.3285332.30164622740792&?454482.2161512.1863652.15Q482.1259402.0955642.065228

g_v- ] 3

70 PERCENT

2.3507962.3960522.4414342.4806782.5155902.5460552.5720292.5935402.6i06782.6235882.6324592.6575172.6390122.6372112.6323902. Q48262.6147932.6025562.5883682.5724682.5550792.5364092.5! 65452.4959642.474520

2.4508672.4963562.5421562.5820182.6 J77542.6492452.6764352.6993342,7160062.7325682.743!802.7500342.7533522.7533702.7503392.7445142.7361492.7254922.7127862.6982582.6821272.6645952.6456502. IQ60662. f335401

80 PERCENT

2.3634282.464994?.5441202 .(20303Z .6930492.7619562.8267012 .867024*2.9427532.9937883.0400993.0617213.1187413.1512933.1795483.2037033,2239783.2406043.2538193363864302709783.2753935.~7733432770143274639

2.4834622.5651632.6445782.7212182.7946412.13644~2.9303652.9920903 .0494e3. I023Q3.1507403.19460032340033.2690493.2998773.3266553.3495733.3668353.3846573.3972593.4068~3 ●4136833.4179363.4196263,419551

12 Jan 1984

2.5?.52.52.52.52.52.52.52.5?.52.52.52.5:* 52.52.52.52. 5> 5;:52. 52.52.52.52.5

2.62.62.62.62.62.62.62.62.62.62.62.6~C6

2.62.62.62.62.62.62.6

;::2.62.62.6

60th, 70th and 80th percentiles of the lognonnal distribution

for means and sigmas from .1 to 2.5 (continued).

SIGMA

.1

.2

.3

.4

.5

.5

.7

.8

.9! .01 .1! ,2! .31 .4i .5;.61 .71 .8I .92.02.12.22.32.42.5

.!

.2

.3

.4

.5

.6

.7

.8

.91.01.11021.31.4i .51.61.7! .81.92.02.1222.32.42.5

63 PERCS’JT

2.5234362.5A29b02.55B537‘2.5700G72.5775g92.5~11742.5609442.5770632.5697302.5591742.5456442.5294022.5107152.4898522.4G7i1772.4426452.4167972.3897602.3617482.3329542.30355622737]42.24357122132562.182879

2.6235102.6432822.6592252.6712972.6795092.6839182.684LS282.6817802.6755512.6661442.653?832.6387072.6211612.6013942.5796532.5561772.5311992.5049362.4775992.4493732.4204362 i3909502A 610592.3308942.300571

7CI ?iRCZI; T

2.5509332.5326342.64281?2.52324:2.7137332.7521652.7804752.3046562.5247552.s408622.653!102.8616562.8667232.6684912.8671972.8630742.8563562.8472772.83 S0642.8229362.8081032.7917642.7741012.75’52592.735465

2.650S932.6988902.7434232.7843672.8215492.9548472.8841902.9095602.9309852.9485372.9623252.9724912.9792042.9826512.9830362.9805712.g754712.9679552.9582372.946524

2.9330!8Z.9I791O2.9013812.6836012.864726

8C F’ERCE::I

2.5 R34?42.5 S5J172.7449852 .8220432. Z9GC762.9667213.0336693.09 S6713.1555403.210i493J!6C4293 .30636.33.3479843.3853573.4186223.4478903.4733333.4951313.5! 34773.52e57i3.5406153.5496153.5563703.5604743.5@.319

2.6835232.7654582.8453542.9227902.9973753.0687653.1366643.2 COI1273.2610653.3172423.3692753.41 7!303.4608173 .5003e93.535s303.5675563.5954063.6196363.6404183.6579313.67236S3.6839003.6s27313.69? 0413.703009

—

*V-14

MIL- Hi)Bti-d7;

TABLE B-V-Ii.

90th, 95th and 99th percentiles of the loRnomal distributionfor means and sigmas from .1 to 2.5.

.!

.1

.[

.!

.!●1.1. 1

I.4.1.1.!.1.1.1.1.1.1.1.1●1

I● .

.!

.1

.1

7. .

.?

.-2

.Z

.?

‘7.-

.?

.?

.?

9.-

.2

.?n.{.

.?

.2

.2

.2

.2

.2

.2

.2

.7

::.?

.! ,2~7523

.2 .??7300*.- ,22!OF3

.4 ●20C7(72

.5 1cF214

.6 :IF77723

.7 ● 17F3F0

1.41.5I .61.71 .FI ●:

2.P2.12.22.32.42.5

:;.3.4.5.6.7.P

Q

I :b

1.11.2[ ●JI*41.5!.6I .71 .FI ●C

2.C’2.2.;2.5?*42.5

7ioQ4627255613?502!544?593?9e?

.135536●

13~44p

.12767F1241RP

:120945. 117?21.115094

112444:IOC052.107605●I053FF.103290

.32770?

.41!046,4499s:.454601.45!04F.442165.43!120419404

:40772$.3F6427

.SF564Q

.375445

.365g22

.356760

.34P227

.3401!?F

.33?.60F

.32545!

.31F684

.312277

.3C6201

.3P0431

.2$4>44

.2pa7J8

.2f4755

R-v- 15

.27?1 12

.36C13f3

.Ypscp>

.3F’6526

.3FIFF!

.!.744C0

.365$44

.3573/6

.3APP74

.340772

.3?3071

.5257P3

.31F?CI

.312402

.306265

.JOC461

.2Q4Q6p

.2ps76fi

.2F4F16

.2FOJ 16

.275641

.271375

.?6730!

.?6:40?,25y67a

.3FC063

.536?24

.&61649

.720766

.752131

.767367

.7730F2

.773053

.76?49$

.76376?

.7566F4

.74P7Q!

.7404s7

.731FF?

.723246,714633.706118.60774p.~p$550

.6P1544

.673739

.666141

.65F751

.6515K7

.6445P5

. 4904?3

.F553A?1.C7916&1.217?031.:SCC601.s6f:*l1.40?67s1.43PCII1.45P74fl1.4733121.4e!57cj,4$@r471.4941541.4sJ6277104C6F54

1.4962141.4s46101 .4c223g1.uFS2531.4F57751.4FI?C21.477713i.4Y3272;.46P62C1.463P30

,536F23.9P09F5

1.3F66031.71109P1.s627642*15P3532.3!2P362.4344072.5330172.6133212.67?2?92,733Q@?2.77?3552.F173592.?4S2S42.?76C222.89F541?2.91747S2.9333572,9466252.95765P2.9667392.97414fJ2.9F@0942.9F4762

12 Jan 1984

MIL-t{Dr\K-L72

TABLE B-i- Il.

?c:h, 95tk, and 99th percentiles nf the loj?, normal discri$utimfor means and si gmas from .1 to 2.5 (continued). -

m-A !’

.<

.;1..1

● .

1. .

.3x

● .

.3x. .x

● .\9.t..

.3●3

1. .T. .\. .\. .t

● -T.<t

● .t*“

. .

.;;. .

.4

.e●A.4●A.4.4.4.4.A

.4

.4

.4.4

.4

.4

.4

.4

.4

.4

.4●4.4,4.4

2.12.22.32.42.5

CC PEPCENT

.4314?1

.542971

.6J656P

.65740:”,676336.6Fl?@l.6795~7.672710.66324P.6523?2.64C’P65.~29j ~6.6[ 73F5.605F,64.5$4641.58376P.573274.56316F.553450.544J[I.535J4@

.526522

.51F?41

.5102E?

.50262?

.53202F

.65541?

.7532?5

.t?zzo?l

.e66214

.F91??7●5@4a59,~~pzp]

.?075?3

.9@2096

.F?4039

.pp4330

.F735F?,FC2240.F5057?.?3FROP.F27CC?.F1545?.F04037

7Q2F54:7i1935.7712$7,760$4F.750F91.7411?4

.4F54f7

.67679]●F.!4J36.949!(I4

1.02F166l.PPI 14:.1.I15F7[].137e961.)51C501.157S4i1.i6C3661.15s579!. 15646?1.1516KF1.1456431.13F73?1.1311P?1.1231?!1.[14s0s1.1064?6l,pa7p32

I,cRs1911.rPo551!.07194s1.0634!4

.fp]p]~

.77PI?.6,CK(’216

1.11244P102?2]9C

!.3222??1*3C 1347

!.4415~21.47FOP41.504?63I .5??53@~ ,5347331.54??611.5461641.5472401.54FIP51.?43?.34\ .53P??5[C%3~6F7) ●%?75p4~o%pf17@JIC513367

1.5056341.49759F!.4??3s7

.5055ssI,C2! 154

1.47}47F1.P?CC452.255?11?.5f5f4c2.e2Fp7p3.(150107L.2J74ss503c7/~~

:.533F223.65161C3.7536223.F423$53.SIS9FI3.cPF~~74,c47yi’24. IC’0P534.14766(’4.IPS!6F’A ,7?f,~:F

4.?.5FF31t.?FPC2C4.314032

4.331?P3

.6FFIOP1.07:646\.%13fp21.!’6197[2.3FFF172.7732063. I17F763,4221953.6F??5?3.c2557~4.,1331KI4.316(.6(a.47935PG.624@724.7532124.F6FEI:4.9726005.cc6@33~e)~p~fas.?266al5.2?57525.35p5cp5.41573F5.~67fc5~.515312

-

12 Jar~i98iII-v-lb

!4LL-I!DDK-L ?2

TABLE B-i’- II.

90th, 95th and 99th percentiles of the lopnormal distributionfor means and sigmas from ,1 to 2.5 (continued).

v&t;

c0/

5● ..5

c. .,

G.,‘

. . .

c. .,

L. .,

%. .c,. .c

..’

5. .5. .

.5

.5

.55. .c,

● .,

:;●5

5. ., ‘.

7. .-.

●

t-.,. c.s.6.6.6

:;.6.6.6.6.K.6.6

(:6

(.-l.6.6.6.6.6.K●K

01.2.3.4.5.C.7.F

I::1.11.2[●31.41.5I .61.7I .F

N2.12.2eL .3~.d

2.5

.1

.2Tw.

.4

.5

.6

.7

.Pc

I;61.1!.2!1.3].41.51.61.7I ●F]Cp

?.r2.1Q-G.&2*J2.Aticf.

.63194:

.76C’CP9

.F7262?

.sf16341.C27C:41 .c7JJP?r’1. IC43751.173C741.1329?71.i365r!1.13534Pi.1J@F311.1239021.1157!5F1.105413I.c’s474f1.0F35.~C1.P72POCj.Cf~2p6

1.C4P51CI.C367611.@251021.C135791.PO?226.>$ ;o~p

.73!6?3

.P62F42

.:F3 12C1.CF5S4?1.16?OOC1.2331371 .2FC7F01.314FIPI.337S$61.3526721.36C7671.363F021.:&29651.35s175].3531431.34541?1.336427I.~264aK1.315PP21.3C47F5I .2$33~(7-

1.2F1730I .26spFe1.25F213I ,2A~45F

fj-~-17

?Q PERCENT

.7772]21.13755C!.5575512.CC51F27..45?4632.PFC5763.27$4423.5451]e~*077~~l4.2777444.54FF$C4.7c36C15.C146375.?145995.JQ5P325.5K04275.71 C2265.F46F445.S71K?56.6F60176ol?oFp26.m??736.375??26.45771?56.533301

.R69P341.21119sI.6104692.04626?2.496460~.g420553.5732er3.7FOOSI4.15SF094.5114224.F354555.!332935.4067405.6577565.8?F2926.1002!46.2952546.4?4?Q?6.640PF36.7s42006.S361077.0676447.IF973F7.3032207,d~FF33

12 Jan 19$4

TABLE B-V-II,

90th, 95th and 99th percentiles of the lognormal distribuclonfor means and sipnas from .1 to 2.5 (continued).

MEAN

.7

.7.7.7,7*7.7.7.7.7.7.7.7.7.7.7

:;.7.7.7.7.7.7.7

.E

.F

.F●F.8●F.8.e.F.F.F.f?●F.e●P.F●E!.?.?.8●F.?F● .

●F.6

$] GF#

●1.2.3.4.5.6.7.P*C

! .0!.!I .2I .51.4I ,5I .61.7I .F

N2.!2.22.32.42,5

.1

.2

.3

.45. .

.6

.7

.?

.9I .01.11.21 .31.41.5I .6!.71 .?I .92.02.12.22*32.42.5

90 PERCENT

.R3t41?,963760

t.oe90061.201145\02969P@1 ,375F201.43tJ660I ,4t!7353! .524Q341.550769!.5694PK1.5F!5!3!.Y?F3Q21.5sI]021.59049e1.5?72661.5P195F1.5750!51.5667901.55756?1.54757?1.5370041.5259941.51467P1.503J2R

.9311621.0640561.1923551.3toF351.4160891.5065S01.5?2S061.6441F21.693677I,7324271,7620411.7F3PP51.79951J31 .FOP?IF1.F15931i.el~4021.F179771.F151871.elo4711.F041911.796645I*7$807F1.77P6941.76F6611.75FI17

95 PERCENT

.p754?91.0670071.2642131.457C22!.6S77121.F@16161.$467$42,0731902. IR19562.274?672.3534~02.41?9S52.4758512.5226FI2.5617532.3941F92.6209492.642F472.6605762.6747222.6F57F42.6?41F42.?002842.7045942.706777

.974251!.1636?51.36030?1.5562S21.7445921.9~04322.0?09172.224F962.3524392.4643??2.561?6!2.6465972.7197212.7R26942.F3676F2.PP30652.9225752.95616@2.9F45993.00F5253.O?.F5153.045@603.C5F58fI3.06?4673*07FO19

99 PERCENT

.9645271.29!44S!.6724662.0s31292.5567@42.9Q762F3.43344F3.?653164.2776!54.66724?3.032>275.3745635.69~F2~

5.9FFF426.2639456.51?5!!06.7571F96.97F1727.jE3e557.3754727.5341657.7209~17.@76F75F.@2272!P.i5930?

1.060533!.3762191.7417?42.14?2922.5FO19?3.0277653.47F6$63.923?404.356?314.7732355.170}795.5464125.9015256.2357526.5497396.P44~9@7.12C7457.3799057.6229F07.F51056F.065175F.266322e.4554218.633332F.60@P5t

-

12 Jan 1984B-V-18

---

90th, ?5rh and 99t~ percentiles of the lopnormal discrib~tion

for means and sipmas from .1 to 2.5 (continued).

1.($I.c!.01.01.01.0!.01.0IOcI.(I1.0l.r1.C1.@1.0J*n

!.0I*O1.01.@1.0I ,0100I*CIn

~:~m~

.1

.2

.3

.4

.5

.6

.7.?c

1:61.11.2] ●S1.4]Oy

! .61.7I .?

;::2.12.22..32.4Z*:

.1● *.;.4.5.6.7.F

I ::I*IJ .21.31.41.51.61,7I ●F] .$?2.02.12*22.32.4~.~

9tI PERCENT

1.030931!.J640471.2942631.417!1C1.52930!1.62F9131.7t52561.7?F57!1.P49705I.FPSFSIl,?402431,9722271.S969P32.0155932.02900?2.C3E0472.0434132.0457032.04341F2.0429F62.05e7622.0330492.0261002.0181292.00?314

1.1307271.263F!851.3953201.52121R1.63P543!.74524S1.S40237].?232671.9046~32.05522P2.1058642.1476392.1816032.2@F7512.229?932.2461492.25793?2.2699932.270E5C2.2750C32.272fl!$32.2706962.?66FF12.2616622.255?S9

95 PERCEPT

].0732651.2606?71.456252!.6s34541.P463922.@3057s2.2021722.359954?.503@oF2.6S!44!2.745FS12.$473112_y3K7c73.0!54F?3.@F44?F3.144E6S~O!?75623.24344e3.2833033.317F203.3476103.37!)211~e>o?c!?p3.4136F93.429353

!.)72456!.35t!1721.5523561.74??5!1.9453142.13474P2.31477?2.4P320?2.G3FP@72.7FII?.O20?lf)2~73.02675?3.13 !3223.224$473.30!z2473.3F743P3.44e30@3,50665F3.55F2703.6038313.6435653,67g2373.7101513.7371573.7606:?

~g p~Rc~MT

!.1574221.464169!.61679?2.2082182.6292233.06940S3.5190403.s696324.4144334.t1482795.2676165.6701366*C34>236.4292016.767!337.C95653?.4063427.69?9397.977272?.239211F.4F6634F.7204C7IT.g4J369S.15C321s.34F023

1.2549321 .55A424I .F?61692.2750992.6F41153.1150623.5596864.010~644.4605444.9049255.3394435.76115!6.16F0456.558PIJ46.9S30157.2902367,63066?7.s54661F.262731C.55548i?F.F336C7?.0977?I9,s4?7s4Q.5F7201?.8{3F20

_—

)!1L-}[UBK-: 7?

TABLE B-V-II. -

90th, 95th and 99th percentiles of the lognor~l distribtiionfor means and sigmas from . I to 2.5 (continued).

FIE4N

I*I1.11.1!.11.110/I*I1.11.1I*I1.1l.!1011.1lot1.11.11.11.11.1}.11.1!*!1.1!.1

1.21.2!.2t.21.21.21,21,21,21.21.21.21.21.2[.21.21021.21.21.21.21.2I.21.2l.?

S 1 GFIh

.1

.2

.3

.4

.5

.6

.7

.?

.91.0!.1I .2I .31.41.5I .61.7

:::Z.@

::;

:::2.5

.1

.2

.3

.4

.5

.6●7.?

QJ :6l.!1.2I .3!.41.51.61.7I.F

;:?’2*I2.22.!!2.42.5

sO PCRCENT

1.2305481.363651].495~611,623916!.7450741.?572?11.9592F72.0504692*\30goR2.2006(?52.260751Z.slle!o?2,3>472(!2.3903632.41?56s2.4431162.4617142.4159972.4F6SS02.493F1O2,49R2742.5003032.5C322F2,49F33g2.494FQ4

1.3303901.4633E51.5960F41.7256P41.l?497231.9662522.0739062.171PF42.2596832.337?992.4066(!62.4662742.5176822,56156(!2.5986412.62?6352.6552132,6759922,6925332.7053442.714F762.7215332.72567!2.7276032.727KOP

1.2717F2I*4559F71.64F7411.F457232.0426402.2356432.4215PS2.59E!1252.7637232.$175253.05!2323,1PR9653.307!323.4143303.5112633,5?~6p73.6773633.74R03!l3.FI 1420~.F6f/1743*9]~9173.?642144.0645764.0404794.07233R

1,3712121.5540?7t.74543F!.94!6692.1391202.S343772.5245042.7071632.F806493.043R443.!96]423.3373443.467567S.5F71463.696569~.7s64153.eF7310J.9~9~964.0448094.1126634.I?40424.2294S14.27951?4.3245974.365!54

1.35ZI!941.6463931.g7P9222.34676!2.7444753.1655633.6031394.C505244.5016664.9513775.39541F5.eso4776.254@e46.6644F97.0605377.44[5537,807232e.t57552F.492?04F.U130269.lle965?.41!0379*6FW019.95583P

10.20?73?

1045II?71.73S6682.06432P2.42239@2.R096703.2209383.6!504834.o$25~74.5416474.992?21S.4421625.8t?59106.3214156.7465757.159F527.5601@27.S46891F.31961FF.67F2469.022F459.3536279.670?109.9750e3

10,2665?610.5458F9

12 Jan 1984 B-V- 20

L

‘..-

90th, 95th and 99th ~ercentiles of che lognormal distribution

for means and sigmas from .1 to 2.5 (continued). —

i.41.4!.41.4I*4I*4!.41.41.4!.41.4!.41*41.41.41.41.41.41.41.4!.Aj.aI,A1.41.4

.1

.21.-

,45. .

,(.7

.PQ

! :6

I*I

1.2] .3].4lo~I .6:. 7

I.F]*$

2.C2.!2.2!~1&,-2.42*5

.1●2.3.4.5.6.7●F’Q

1:0!.1I .2I .3]OA

1 .5I .61.7t .?I ●Q2.C2.12.22.32.42.5

1.5301271.6C2E3F1.7s60071.~27520

2.05541$2.17F0122.2939612.4022902.5~23eP2.5~3g6@2.67CQ$32.7516412.PIP2722.P7731$2.$2!+2P62.5747~7~.o141243.@4pof73*@770463.lr153s3.1?1ss0:.13FP II3.1523763.163(’265.171070

CQ P[p~~LT

1.54976[1.?ss959?.151?402.5@130c2.F’75F442.2PoP7fI

2.7C2C4Ct

4.13760$4.W27315.C32?CC5.4P41!75,a3?cQf76.376~036.?122817,2Jp73~7.6543986.05e2~sF.44s7@lF.F2F452S.194131$.546PC40.PF65Ps

10,213701!O.52~42P10.?31!13

1.64F’5301.929C532.241C4P2.5?2P?P2.9519943.3449313.75?7614.l@625@4.62616F3.@734@s5.52422!5.9752566.4236236.f166P?57*303C9C7.7306328.14F311F.55523P?.950761?.3344???.7C6?21

10.065?$5JO.41344410.749i2~11.873!10

12 Jan 1984

Y!!. -}{!)D}’-L?2

TABLE B-V-II. -

90th, 95th and 99rh percentiles of the lognormal distributionfor means and sisrmas from .1 to 2.5 (continued).

MEAN

!.51.51.51.51.51.51.51.51.51.51.5],y1.51.51.51.51.51.5I*51.51.51.51.51.51.5

1.61.61.61.6I .6i .61.6I .61.6I .61,61.6!.61.61.61.61.6I .61.6

;::1.61.61.6I .6

s] Gmn

●I●2.3,4

●5.6.7.F.9

\ ,0J*II ●21 ●31.4!.51.6J.71 .F1 ●92.02*I2.22.32.42.5

:;.3

::,6,7●Fa

I:61.1I .2I ,31,41.51.61.7I.?] ,$

2.02012.22.32.4

2.5

90 PERCENT

!.6300!61.762S74l.eswm2,02792?2.1571042,2F18272.4008032.5130452.617P652.7J4F?557.eo3e542.FF490120$5@1933.0240423.@F28423.133C333.lFIOF13.22145?3.2566303ei?e70443.3131263.3352743.353e593.3692233.3F16F0

1.729916;.P623231.9s56012.12E1122.25@2B92.3F47112.5061632.62)6702.7305032.P3217F2.92643C3.0131803.09250p3.1646123.22?7gl3.2FR3653.34075321.3P73553.42FSP53.464P543.4965603.5240?23.5477?0J*567cp9

3.5F5P22

12 Jan 1984

?~ p~Rc~NT

l.66?o321.84966!2.0372572.2305152.4270F62.6246272.F209233,013sP63.2021213.3?3$543.531?4343.7?4FI?3.FF26124.0315F74,1716814,3029P44,4257034.5401294.6466064.74551e4.8372704.9?227?5.0009345,07s6573.140?29

].7gs6071,94?5032. I?50212.3272502.5231412.77061?2.9176F53.1125033.2P34563.41791P53.C6F’5973.F4CF654.0P54014.161F344.30?s774.44?7934,5013674.7C4F794.F?C5764.92R7585.0297565.J239215.2116135.2$31955.SK9C?7!

99 PERCENT

1.7474642.0247962.3316362.6667323.0279973.4126493.t?173904,23P6124.6?2~9~5.1156’125.5643R16.0155456.4663396.9! 43117.3573FF7.795?54P.22232?6.64J 7279.05J2259.4502279.F3F325

10.21527210.5?095110.935353I 1.27F556

1.8465322.121C662.4233622.732A573.t066103*4P35P93.FF06084.2~45?44.72226?5.16039F5.6C5F076.05552$6.3068336.9573727.40497??.847FFoF.2f4%’3F.713F639.1347439.54646S9.94F475

10.3403WI0,721F56I I .0c2tT2411.453212

FITL-iiDBK-&;~

TABLE B-V-Ii,

1.7!.71.71.7].71.7!.71.71.7].71.7].7le?

1.71.71.71.71.71.7

90th, 95th and 99th percentiles of the Iognormal discribuciocfor means and sigmas from .1 to 2.5 tcmcinued).

1.71.71.7],71.71.7

I*P1 .F1 .FI .FI.F1●FI.FI.Elog1*FI.R1 ,F1.FI.F1.?1 .F!.FI.FI.F1.FI.FI.PI.@l.!?l.F

s] GFP

.1

.?.

.3.4

●. .

.6

.7

.?a

1 :i

1.1

1.2I .3!.41.5I .61.7! ●F1.92.02.12.22.32.42.5

.1

.2,3

::.6.7●F

e1:6!.11 ●2I .31.4I .51.6l.?1 .PI .9

:::2.22.32*2.:

~@ p~pcENT

1.f2?F27l*9520p62.C$53~7

2.Z2F1552.35s1(’22.4F6FFS2.6!03752.?2s6132.F40F612,$465F5

S,0454433.13?2673.2220593.29sF593.370s2?3.4354933.4?3?Ff!3.5464503.5?35443.6355363.6727923.7C56663.7345003.75?6173,7F1324

I .92S7462.061F622.j9507p

2.32EOS32.45?63?2.5FE!5252.7136F?2.g34zzo2.S4937F3.C’5F6023.1614973.257F263.3474?23.4305123.5@69??3.5771423.6411F4306$g4103.7521293e7@96623.F423393eFF04p63,$]4422

3.?444533.972F75

95 pFRr~~IT

!.F6?3!F2,0474652.2!?.?F72.4242142.61S34F2.F 165473.Q14P073.210C’3F3.403!!73.5?1S233.775Z563,9525594.122?!04.2P57Q34.440s264.5FFs?)34.7??9054.F?S71R409p393]5.l@075s5.2104605.3!33255.4C96&05.40?7F25.5F4013

l*9&po592.1465302.3311302.5?.1$?42.7157332.9125C33.! 100793.3@690?3.50!566~c~027fJ43.F794764.QK07454.235PF04.4043454.5657664.719?0sA.P666635.0060175.!3R0435.262FFI5.3F@71?5*4$17g35.5$6327

5,6?4622507F04Q

?s PERCENT

109457102.2177732.516C34~*p3p7jc3.IF745S3.5573543.9470764.3539FI4.7752375.2C79445.64?2356,~$63676.54677P6.9PF1367.44P35F7.E95625F*33F3736.7752829.205264s.627437

lC.04110210,445728IG.P40?2211.22641511.602041

2.044?F02.314P442.6C95022.92F33~3.2702313.6335S74.0164624.4165554.E314075.25F4455.6s50F5

6.13F?066.5872137.C380P07.4e93et7.93930”8P.SF6257?.F2PF659.2C5S5F9.696557

19.l~9F6319.53523219.942!6111.3402731 [.729294

Yii.-l-il)! ?.-+;:

TARLE B-”,’-II.

90th, 95th and 99th percentiles of the lognormal distribution

for means and si~mas from .1 to 2.5 (continued).

mAN

]*:

1.9I*91.91.91.91.9I*91.sI*$log1.91.9

;::l,?!.9j,~1.91.9I.g1.91.9[.?{.9

2.02.02.02.02.02.02,P2.02,02.02.02.02.02.02.02.02.02.02.02*P2.02.02,0

;::

12 Jan 1984

S 1GMA

01.2.3.4.3.6.7●Fa

I :6I*JI .2I .3

M1.61,71 ●PI .92.02.12.22.32.42.5

,1

::.4.3.6.7.F

1::1.11.2I .s1.41.51.6!.7I ●PI .92.02.12.22.J?.42!.5

2.0296722.1616522.294F032.427?5C2.559c6F2.6P97442.F 162972.95t75e3.C564023.16P6553.2750P73.3754123.4694673.5572023.65?6603.713962?J.7F32P63.C46~573.9049333.9577s14.0057204.0490164.0F?g724.12287S4.154005

2.1296042.2614552.3945202.5277712:6601412.7?06392.9183443.0424363.16220?3.2770F73.3866213.4904F63.58F4723.6PC4743.7664753.E1465353,9207753.9P?3664.0525154.1104564.1634394.2117??4.2555P54.2?52764.35106F

93 PERCEPT

2.06FF272.2456832.42?4322.6167762.13123043.oog5473.2060333.403S423.59?144~,7$22~43*51#lj5544.1662064.3454504.51F7044.6P55304.8456254.99QFO05.144?695.2F412S5.4163465.5417445.6604905.7727825.e7f1845S.S7F920

2.16?6182.3449122.527P732.7163432.909063S.!047123.3019603.4995033.696105S.F~Q6204.0$20554.2694954.4522004.6295564.F@loFl4.9664165.1253115.2776145.4232565,5622415e69463~5.t??05345.9400996.0535056.160fJ4P

99 PERCENT

2.1443272.4122232.7P36453.OIPIOI3.J546673.7120124.C)FE4564.4620474.$9C6225.3119025.7435646. IF33056.62E?O07.07F24$7.3294037.9F05F7F.4302138.P76P76S.31935Fs,7566!3

1001t!776010061206~11.02F94311.43191211.83F60?

2.24373S2.509P642.79P3643.1oee4P5.4405463.7923374,1627864.5501994.9526675.36F2305.7947416.2301246.6723247.1193717.56S411F.0207278.471755e.92]oee9.3674g3?.P09F50

\oo~4725110.67FFe611.lo40e711.52230211.933(W7

R-V-7.4

HIL-ni)f’JL-”i2

TABLE B-V-T[,

9f)t!7 , 95cII and 99th percentiles of the lo~normaj distribuclonfor means and si~as from .] to 2.5 (~~ntinued),

2.12.19 ,. .7~.i9,Lot2.1-<.!:.1?.12*!2.17.12.1:.1?.!2.12.1.->c. 12.12.12.1?.12.1?.1291

2.2-J*L.*12.22.22.22!.22.2?.22.??.22.22.22.22.22.2?.2

t

:;3. .

.4

.5

.6

.7●Po

I:;1.11.2],31.41.51.61.71.F1.92.0?.12.22.32.42.5

.1

.2

.3●d.5.6.7.?c

I:iJ.]1.2]●J

1.41.5I.K1.71●P

;:;2!.1?.?2. 32.42.5

2.22?543?,361270

2.4?42s62.62754F2.7601952,F$12F()

3.0199463.145418S.267@lF3.3F41763.4964323.6034363.704?413.EP07973.F?os4@3.9753764.0541764.12’74614.]~53a24.25e16(l4.3159794.3690764.4176$04.462C604.50242F

2.3294F62.46]0?72.59~9?l2.72?3022.F601602.??17223.1211913.2476363.371OOF3.49014F3.60479&3.714W33.?1S2373.91e5744.0124F64.1009384.1F3956~.2616164.3340374.4013714.4637?44.52!5014.5747034.C?36!54.66?4S3

2.2684272,4442Fs2.G2645P2.F14CFI3.(’06CPL3.?010?!3*3~7:2)3.5?75093.7~26JF3.9p~2424. IF134C403710K74.5566764.7375364.?131355.n9sc17Q5.2470435*4p4p8p

5.55636!5.70!5265.FA@3555.~7ppQ76mp>$~59

6.21?57C6.*>JJo~g

2.36F2532.5435G42.7251152.9119743.1031213.2?74F3

3.4$s?563a6aj4~5

3.FFF8fz?4.0P52F04.27$6924.4712P54.6593224.F4316r55.0222R65.l?625fI5.J~4720

5.527446S.6F4257

5.FS504Q5.97:762K.IIF4K56.25]]5]6.>77~~,~6.49F9~6

2.3432@72,60772?2.6S35FG3.~OC446L.5276P63.F74346G.25Q1968.5207655.0173975.4272>s5.64F5?76.2733F76.7177817.15194C7.610113‘P.@60654P.512040P.962FP3?.411?34?.P5FOP0

10.30034310.737F74! 1.169?4P11.5S5?4F12.015363

2.4427242.70S7~92.9P?227!I.2927P63.61592?3.957F444.31746E4.6935225.0F45465.4FFP515.$05(!536.331]276.7654377.20627F7.652004F.1010498.s519449.C03333S.453?76S.902754

IC.34F66FIC.7SOF3511.228486I 1.6C095512.0F7674

12 Jan 1984

.-.-}Ili--l{[!i{ t:-+ I-

TA3LE E-I’-::.

9(lth,95th ad 99th percentiles of :he lo~normal distributionfOr means and sipmas from .1 :0 Z.5 (conticud’)—. —.

FIEAN

2.32.32.32.32.3

:::20 32.32 ●32.32.32.52 .s2.32,32.s2032.32.32.32.32.32.s2.3

2.42.42.42,A2*A2.42.42.42,42.42.42.42.42.42.42.42.42.4?.42.42.42.42.42.42.4

1? ;ap 19?4

SIGMA

.1

.2

.3

.4

.5

.6,1.?●9

1.0l.!1.21.31.41.51.6),71 ●F1 ●92.02.12.22.32.42.5

.!

::.A.5.6,1

.F

1::1.1I.2I .31.41.51.61.7J ●elea

2.02.12.22.32.42.5

?(I p~Rc~NT

2.42943!!2.5609342.6937542.e270412.96005F3.0F20013.22Z1473.3497913.474S!83.5?5!88

3.7119393.F?41973.9316714.034)474.1314F74.2236194.3105314.3$22594.46eeF!34,5405194.6073094.66S4174.72?0244.7F03204.F29503

2.5293F52.6607@l2.7?341?52.9267703.0599053.1021693.3228713.45136TS.5770663.6994453.fft60513.9329044.0425024.1476114.241F26F4.34S7694,43426P4.5197704.6003204.6759?ff4.?469184.F132114.e750334.9S25474.91?3930

“ f-l~,-’”-.

—

95 PERCENT

2.46t?0942.6429712.F23F903.0100093.2@04043.39410!

3.5900933.7F73743*>p495g4.lf19054.3773344.5704384.7604954.$468735.1290305.3065135.47P9555.6460725.$076535.9635536.I136FF6.25F0256.JJQ65776.52?3?26.656553

2.56794R2.7424242,$22754

3.loe173J.2Q~0443.490875S.6B6S433.?F333P4.0F092R4.?7F2404.4744394.66F7554.8604F65.04?OOP5.2337775.414S275.5S02715.7612975.9271626.0F76FF6.2427516.3Q22F3

6.53625P6.6746F96.F07625

99 PERCENT

2.3422t42.RC)4C17S.C8924~:.3F5?753,7051454.0426624.s974074.76F26U5.15593?5.S530215.9640016.3F53136.8153667,2529847.6954258.142406F.502]23

9.043260$.4946019.945033

10.393549\o.g3924e11.2F132?11.719015612.15191S

2.641F@02.9023933.IF15993.47$3363.7952214.12F6564.4781?414.P44?965.2253?35.6!934!6.0253126.441@766.8675!!07.3009667.1405978.lf35074?.6330629.DF32949.5345!$s9.9FW41

10,43605(!10.S~432411.329F21li.77fe2012.209677

-

?IIL-HDBK-L72

TABLE E-V-::,

-.

90th, 95th and 99th percentiles of che Lognarrdl distributionfor means and sipmas from .1 to 2.5 (continued).

2.52. . 52.52*>2.5?.5?.5

~2..2.52.5?.52!.52.52.5?.52.52.52.5

2.5?.fl2.52!.s?.fl2.52,5

2.62.62.62.62.62. 62.62.62.6?.*K2.62.62.62.62.62.62.62.62.62.62.62.62.62.62.G

SI GYA

.1?. .7..

.45. .

●f.7.r

1::1.1I .21.31.41.5I.61.7I .F].~2.02.12.2.-.*,.52.42.5

.!

.2

.3

.4

.5

.6

.7

.?Q

I :6

1.1

I .2I.3]*A

!.51.61.71 ●e

;::2.12*22.32.42.5

90 PFPCENT

2.62934P2.760&~72.F:32453.P2&4?G3.15:7133.2c?2323.4234073.5526313.6793453.??3C443.~232p~4.03?6934.151?534.259F’204.36310P4.4616904.5554QS4.6444?14,72F69?4.P@F16$4.ps29el4*?53p445.01?OP35.0F@6405.13F070

2.72929P2.F605C22.gs30j43.1262203.2594Q43.3$?2173.5237FR3.6536373.7E!!2313.9(i60FF4.0277774.1459244.?.602134.3703FP4.4762494.57764?4.6744s]4.7667244.P543374.9373545.(’158315.0F?F4!?5.15?5075.?249275.2B6241

os fJFf?cFNT

20667F]~2.P41sl~3.P2!6??3.?n~4553.3c542c3,5F7FC23.7FP.7333.>703674.176F574.374:7F4.5711454.76K4214ep5~53p5.14?FK05*336p6$5.>2@C?65*~9clll5.F736106.04331G6.20F0206.3C757@6.5218626.670i’3S6.F144F06a95~Fol

2.7G76FF2.Q4144V3.i207i43.304P4?3.4931503.6F4F7K3.F7?25C4.0754F44.2727PF4.4703944.66756P4.F635F45.C57F1F5.24$6645.43F5905.6241225.FOW515*9p34316.1565736.325C’466.4FF6716.6473176.FP@Fs7~6~A?~~l

7.0!26?5

09 PERCENT

2.74150F3.oo@9903.27?2403.5734C23.Ff’C(?6@4.2156?F4.5616194.522y595.29?7115.6P774e6.0FFE4S6.500724S.9220457.35146F7.7f’7655P.22?2?3F.675!15S*123?I0S.57453110.02S90910.47705210.92705111.37507911.F203FF12.262313

2.F41165;.pa95zI3.3751393.667?173.9775F0403036FI4.64560$5.0026@l5.3737645.75FOFF6.1544726.56174g6.97F69$7.4040FF7.v36670fi.27521FF.718534s. 165462SI.6i4901

lC.0G5F1210.51722310.?6F23411*41FO1711.B65F1712.310950

-

MIL-WW-472

-.

-.

APPENDIX C

ACCURATE COMPUTER Hm., (4) ANALYSIS

10, This section describes a method for predicting M~a= $ when anaccurate representation of the overall repair time distribution is desired.The prediction requires that a distribution of time for each maintenanceelement (i.e., preparation, fault isolation, etc.) be ancnrnor assumed,

The prediction ts general and can be applied to any definable distribution orcombinations thereof, however, the complexity of computing the overalldistribution Increases proportionately with the complex~ty of the maintenanceelement distributions, A simplifying assumption cac be made that allmaintenance elements have normally distributed times. This slmpllfylngassumption !s reasonable since each maintenance element Is the sum of manyinde~endent task times, e.q. the maintenance task “preparation” may includetime’for equipment war&up~ acquisition of necessary t&ls, etc. by thecentral llmlt theorem In statistics, the distribution of the maintenanceelement task time approaches a normal distribution as the sample size ofIndividual task times increases. %asedon this assumption the detailedprocedure has been developed and a computer program written for computingdesired IIL..(0). Programs based on other distributions of maintenanceelements can be stmilarly developed and programed.

the

10.1 General a~proach. In the general approach, we have a system with totalfailure rate X,. and with N x J possible repair tyges with random repairtimes Rnj, n-l, .... N.J-1, h.., J where J’is the’totai number of uniquefault detection aud ~solation outputs and N is the total number of repairableiterns. Let A., be the failure rdte of that portion of the n“repairable !tem which is covered by fault detection and Isolation output :Further, let f, (t) be the probability density function for R.j. n=l. .... N,

n~~-i, .... J. It !s assumed that f. is continuous and concentrated on [O,W).

WJ

If T 1s the system repair time, then its density functtcm gt(t) (sfnce theevents T = R.j are mutually excluslve) 1s:

●

g, (t) = I Pm, f, (t) (1)n~

where:

-

r-v-l

12 Jan 1984

t41L-HOBK-472

The mean system repair time is-

where

p, ~,= E(R.l) = mean repair time R.j, and the variance of the systemrepair time is

(2?

(3)

●2 z

= z P., (0, ‘+ p, ) - p?n~ n~

where

p. 2 = var\ance of the repair time R.J.n~

Values of Mma. (4I)are given as solutions to tne equation

●

✏

Mma” (~)Mman (0) gT (t) dt = 1 Pmj f“ (t) dt=o (4)

o n.J

which are not, In general, un~que. Sufficient conditions for the existence ofa unique solution are that f.,(t) > 0 for all t > 0, n-l. .... N, ~=1, .... Jand that each f.j(t) be continous, conditions easily met in practice.Equation (4) can easily be solved, under these sufficient conditions,by using Iterative means on a computer.

10.2 Assuwtlngnormal densltles for the R.,’s. In practice, Rfij,n-1, .... N,j=l, .... J are sums of several independent repair element times whichare themselves sums of a large number of independent repair task times. Anapplication of the central limit theorem suggests that the denslttes fRare approximately normal. -j

Specifically, the density f. will be (approximately)-l

f.,,(t) =

++-- “’{-’( ‘~:’)21 -

12 Jan 1994 c-v-2

tI!IL-HDBK-472

~- where

pa and OR 2 are the sums of the elemental repair time‘J n. .

means ano variances, resr)ec:ively, Presumably, u, artdo. z

wilpos

‘J *J

be such that the normal density is, approximately, concentrated on thet!ve real axis, i.e.,

r

1 \ ‘IJ J J

(5)

If we let n(t) = 1~2fi f e-x’/2dx, then equation 4 becomes

m

which will have a unique solution for all O where O c 4 < 1. The advantagehere !s that only one dens!ty function need be p?ogriwnnedin order to cacuiate(4) using a computer.

10.3 Computer program. A computer program listing is provided In Table C-V-I forDerform~ng the normal case described above. A sample input/output for the program isshown in Table C-V-II. The resulting distribution for the example is shown in FigureC-V-I .

The means and variances for each repair element which makes up the individual repairtimes R., are inputted. p. and o, .,2 are then computed

I’J

and equation (6) is solved for Mm,, (0) for the given O using the secantmethod. The secant method solves equations of the form

f(x) * o

141L-MDBK-472

by forming the sequence (for n-~. ?, ...)

after choosing xc and xl as startin9 points. The sequence is terminatedafter the desired accuracy is reached. Several points concerning the computerprogram deserve discussion.

First, no lntegra~lon is per$ormed per se in the calculations of

Instead, the followlng approximation is used

f-x2/2

n(t) =+-” ‘ “

. ,_ (&i e->/’ [b,A+ b7A2+b3A3+ b.A6+bsA’] +,(t)

where

lc(t)i~7.5 x 10” for all t and

A = 1/(1 + 0.2315419t) with the b,’z g!ven by:

b, =0.319381530

b, = -C.356563782

b, _ 1.781477937

S. = -1.821255978

b, - 1.330274429

-

c-v-4

MIL-HOB~-472

second~y, the user must provide two initial guesses to M.,. (0) denoted byXO and Xl in the computer program. It is essential that XO not equal xl sincethis would cause “zero divides” in the Pro9ram. The be$t way to pick Xo andxl is to estimate an interval which ~m,. (@) ui’1 lie. Then, select XO

and Xl as the enopoint: of the interval.

Final~v, although tne Present discussion deals with double subscripts n and j,t4e d~~tinction~ indicated by these subscripts and independentcalculations performed. Hence, the progran uses the data it?:;dimensioned arrays of length N x J.

The input data is read in the following order:

XO <Initia’system failure

N1 (Number

of thengle

esirnation), Xl (Ifiitia! estimaticm;, ‘HI ($), LT (Totalrate

of e ements contributing to firjt R). LAMBDA (1) (Fai~ore rate)

W, SIG2

Mu, SIG2

(mean, variance for first element)

(mean, variance for 2nd element)

. .

. .

. .

W (Number of e!ef!!entsccx?trl!?utingte second R!, LAMBDP,!2) (fai!ure rate!

MU, SIG2. .. .. .

The following condition must be met:

I LAMBDA (I) = LTAll I

Sample input/output. and program listing follow.

TABLE C-V-I. Listing for camputer program to cqxste M-(0

vhen eiesoental maintenance activities are normally distributed.

000100002000030noo40c,00s0c0004000070cO*OSOOoo?o0010030001100012000t3000140001 soOolbocOot?oc00100c00I?000200c0021C00210m0023000?40 10

002s0002W00??040002s000290c~o:ao00310003?00033000340“W003s0oo3bo1043701oo3@o003900040000410

lrrLICITRFAl*8(A-M~,RE~L*9(0-7~RML*BR@,S16X,W,SX:2,~.L~~M,LTconRoNW, LAM#M(loo).M(loo),sIsi*flw).lTDIAIO,X1AM INITIALGUESSESTOMAX(PN!).LT!STOl&LF41LuR[ KATE oF;“fSTEM.

R[hP15,@)XO,X1,F’’NI,L1ERR=RaIERR(ISIIIRMA1(WI)tRR=U.00W0J.OJ,$,lBEAO(S,*,fNLI=lO)NN,L@lIW(JlLhNBDh(J)-%MDDA(J)/LTWF(.ll=o.ooSIG2R(J):o.BO8020S=1,N9NOISTHEWNSSROF[LEKNTSTOFaLWI.LMSRA(J)ISTJIEr41LLJREMTE OfTWEREPL6CEARLEITEffUNOS[tEPAXRIlnEISMOE U~OFW U[NH7S UiICfiFflLIOU.

RfaD(S,*)IllJ,SIG?muIsTNEHff3h, sm rs wf wwaw or[MM ELEFKMT.

MURIJ)=lf~(j)+MUSIG2R(J)=SIG2R(J)+S162601030lTOTAL=J-1ru=xlxH’tl=xo:N1=XN-(XN-XNN1)*f(IN)/(F~XN)-F(XtWliiURITE(6,2)MlHRAX(FHI)ISPRINTIOATEACHITERATi ON.

]ff YfiPs(IN1-xffI .Lf. [W) GO TO58xilMIxxNlM=lU1601040tONl]t!IJ:LIKI?t(~,l)PHI, XN1F~MATil A, ’W~X(”, F4.3, ): ,;?.2)FoRflal(5x,Flo.2)STOP[mFuNCTIONN(l)Is4rLIcITtEAL*B(A-M,*).tEu=t(O-2)

004?0 C SIMBAMI NOMAl DISTRKW!ON :l”UCTSW00430C rORTK NET140D,SEE 7!4[ tthTIONALPLIHAUOF STAi~WR@S00440c NMDI09UofMTWMTICAL rumzo~s004s0oo4bo00470004B0004?000s00003Io00s?0005300054008ss010540Oos?o00ss010005?000610004)o

. . . .

Input Data

Output from Program

TABLE C-V-II , Sample input /out Tut data for~ax(~) computer program.y

7.OIJO 9,0D0 .90110 250.ODG4 SO.ODO2.OBO .24D0z.~~o .21D0I.eBo ●20D02.100 .18D02 100.ODO2.7~o 15[103.ODO :14B04 50.ODO1.SD() .10DO1.4D0 .08D01,7D() .llLJO1.9D0 .0900~ 50 .Ono1.ODO .05D01.3D0 ●80D0

8.17

b.o?8.108.10

MAx(.we)= 6,10

Mil. -fii3lJK-L7?

-

\

0 000 2.00 ● 00 600 8.00 1000

FIGURE C-V-I. Resulting repair time distribution for a samplo

svstem containing four (L) repair~pcs withdifferent normally distributed repair times..-—..

12 Jan 1984 c-v-8

MIL-HDBK-472

APPENOIX D

AcfJJRATEMANUAL M.,, O ANALYSIS

iO. An alternative to the accurate computer M-., (4) ana]ySiS \Spresented. Tne previous technique, Appendix C uses a computerized, iterativetechnique tc solve the equation. A complete development of the proposedmanual M~,. (@) technique is given here. The technique is illustratedusing the prediction example described in paragraph 10.3 of appendix C. Hhere~ossible, the same terminology and abbreviations used in paragraph 10 of thecomputerized technique are also used here. Tuo alternatives are given forhandling large numbers of

a. Reference is madewhich speeds up the calcu

b. A method of groupprediction example.

types of repairs:

to a progranunablesllde rule calculator programatlcm procedmes.

ng the data is described and illustrated uifh a

20. The manual H-,, (0) analysts is based on the same two basic premisesof the computerized technique. Before giving these premises, SOfIWkeyterminology is first defined. There are NxJ possible system repair types withrandom system repair times R.j, n=l, .... N, j-l, .... J where N 15 thetotal number of repairable items and ~ is the total number of unique faultdetection and isolat~on (fD&I) outputs. The system repair times R.j arethemselves the sumof the applicable maintenance element ~/ type times E-

-J

tiherzm +nd!catez the element type and where the element types are defined asfollows:

a. Fau

b. Fau’

t localization

t isolatlon

c. Disassembly

1/ This element of repair time has untts of hours and should not be confused~ith the probability density element introduced later, uh~ch has unit$ Ofprobability.

d. Interchange

e. Reassembly

f, Alignment

9 Checkout

The first premise is that at least the mean (wC ) andm

Tf cactiof the i. are kq~wfl. 21 The second prefaisen~

-

variance(UE 2,m

is based on the central

limit thenrem which suggests that the pdf of each of the ind~v~dual

approachesa Po”mal dlstrlbu?~on with a wan (PP ) f~rmed from then~

the respective (PF ‘s).m

Mprmj- z pim

M

RfIJ

sum of

(1)

where 1 lndlcates the sum Is taken over all appl~cable element types and a

vartance (un 2, formed from the sum of the respective u~ 2’s jln~ m

(2)

~1 The obvious additional subscript nj is ~~tted on ~E and or zm m

throughout the dlscuss!on,

jJ In forming the on “s as the sum of the respective UC “s, themJ *

variables are assumed to be uncorrelated. lt !s noted that It !s not

essential to know the dlstrlbutton of the Em times, merely their

12 Jan 1984

D-V-2

.—

MIL-HDBK-472

30. Both the computerized and the manual calculation techniques are subject !to the same inaccuracies inherent in the assumption of normality. Althoughthe central limit theoremis evidence that it is app’-esuits) for tne type of s

used and the percentile va’P*ma. (0) for the case justhigher percentiles - i.e..

s usually applicable only for large numbers, thereIcable (le., its use gives reasonably accuratetuation treated here when as few as six E* ‘s arem..

ue Is not larger than 95 percent. The accuracy ofrefered to does decrease sign!ficact!y at theat 99 percent. Fort~nately

requirenients are usualiy limited to 90 or 95 percent.

40. Let f, (t) be the pdf for the system repair timesn~

pcssit!ledifferent f. it)’s. By definition, the fQ (t*; r.;

M~.. (0)

Rqj. There are NxJ

are non-negative

functions whose integrals, when extended over the entire t axis, are unity.

For a given fn (t), the probability that the nj’h type of system repairmj

is completed In the infinitely small interval (t, t+dt) !s f~ (t) dt. The*)

quantity fR (t)dt Is called }he probability density element at the point t.~j

The relative probability of the nj” type of system repair occurring, P.j

is:P., WA.,IEA (3)

Mhere Xnj ts the failure rate In failures per million hours associated

with the n.j” type of system repair and 1A is the total system failure rate

of repairable items, ~1 P.j is also the relatlve probability of the nj”

probability density element, The combined probability of nj’h type of

system repair occurring and being completed In the Intervals (t, t+dt) is

P.jf~ (t)dt. The combined probability of any of the NxK possible systemn~

repair types occurlng and being completed \n the (nterval (t,t+dt) is

~1 Note that P.j is based on all failures and repair procedures that leadto system repair nj. A particular P., may result from failure of asingle component, several components in series, several redundantcomponents, or some other combinations of components. Thus, any system,whether formed of series, redundant, or some other combination ofcomponents may be analyzed by both the computerized and the manualcalculation techniques providing the X.j values can be determined.

MIL-MDBK-472

(since the R., random events are mutually excluslve) the sum of the relative

probabilitle$ of each of the NxJ possible probability dens!ty eleIWntS

multlpled by each corresponding probability density element at time t. This● ● NJ

is lP.jF~n\t)dt, where t = I 1. This expression Is then-l j,l

probability system repair, completed in the t~me interval (t, t + dt). lt Is

also the system repair probability density element at time t. lJslngthe●

probability density element definlticm given above, lPmjf* (t) 1S the pdfnJ

of the system repair time T, i.e.,●

g,(t) - f.”ft) - IP.,f* (t) (4)nj

●

50. Before using lP.jfe (t) as the pdfof system repair time T, ltmustnj

be shown that this function Is a pdf - i.e.. that It !s non-negat!ve and its

integral over the entire t ax!s is unity. Since It Is formedfrom the sumof

non-negat!ve functions, this function !s also non-negative. The Integral of● m

the function over the entire t axis 1s lP.j~ f, (t)dt. This iS justo n~

the sum of the relatlve probabllittes of each NxJ poss~ble system repair type

probability density elementmultiplied by the Integral, over the entire t

axis, of the pdf of each NxJ possiblesystemrepair type. As stated In

paragraph ~0, these Integrals of pdf’s are by deftnitlon each unity. Each of

the NxJ possible P“j’s In the function are thus multiplied by unity and the●

Integral, Over the entire t axts, of the function becomes just XP~j. Th!$

1s the sumof the relatlve probabll!t~es of each NxJ possible system repair

type probability density ele~nt Occurring, and th!s sum, as uith the sumof

any complete set of relatlve probabllttes, Is unity. Thus, the Integral of

.

the funct!onover the enttre t axis fs unity.

12 Jan1984D-V-4

MIL-HDBK-472

60. Let the cumulative distribution function (calf)of T be G,(t). Bydeflnlt{on of the relationship between the pdf and calf:

*tJ g?(t) dt -G,(t) (s)

o

S\nce GT(t) IS the probability of ccmplettng system repair at time t orless, it follows that:

J

Mma. (@) ●

r

m,, (0)g,(t)dt = lPnj f. (t)dt = 0 $1 (6)

o 0 n~

where Mm,. ($) represents the value of t at whtch the probab[llty ofrepair is Q.

70. The integral

type nj at time tof repair type njlet

F“,(t)

JM**.(O)

f~ (t)dt Is the probability of completing repairo n~

or less. This tntegral !s also the area under the pdf curveup to (at) a particular t value. To slmpllfy equation (6),

J

Mm..(~)

D f. (t) dt (7)o n~

Equatton (6) becomes

J

Mm,, (@) ●

gr(t)dt - W.jFmj(t) =0o

~/ This is equation 4 of paragraph ?0.1 of Appendix C.

(8)

D-V-5 12 Jan 1984

MIL-HDBK-472

Note that the derivation of equation (81 hold; ‘or any dls:ributlon of R.j.

Thvx, !f the form of pdf of the R.j and the parameters necessdry to

cnaracter:ze the pdf distr~but~on of the R.j are known, bcth the

computerized and the Inanua? C?lCUldtiOn tect’n;ques can De uses without

assum~ng the adf of each of the ind:~idua! R., is normal.

80. TO so!ve equation (8), :t is necessary only to find thE t val’)efor uh’cb

the ~um, over all NxJ poss;ble system repair types, of ~,F,Jt~j gives the

desired O. Valtjes of +., are calculated as iod!c~ted by equation (4!.

Values of F.,(t) are found from tables of area under suitable pdf curves.

An Inltal t ts selected and evaluated. Successive t values are then

until the des~ref.iQ Is obtained, to the desired level of accuracy.

90. The p,ed!etion example used here to illustrate the manual calcu

technique is the example described in paragraph 10.3 of the computer

examined

ation

zed

technique. The individual R.j are assumed to have normal pdf’s. Table

D-V-I contains the input data for the E- comprlsing each nj system repair-J

type, plus the PI and U[ ‘for each E. of each nj system repair. .

type. Usfng this Input data, the individual nj system repa~rtype iJW .2

~j

ok and P.j are calculated as described above in paragraphs 20 and 40 andmJ

as indicated in footnoes !/ through Ii of Table D-V-XI. Columns 2 through

respectively, of Table O-V-II present these calculated va’

individual nj repair types. Columns 5 through 8, respect

D-V-II present the calculated values of F.j. P.jF.j and O

ues for the

vely, of Tab e

for four

iteratively-selected trial values of t. As shown, the desired @ value of

4.

--

0.90 Is achieved at 8.10 hours. This is the same value given in paragraph

10.3 of Appendix C for the example computer output.

12 Jan 1984D-v-6

MI1-HDBK-472

ction example described above indicates the relative simplicity

of tne mtirlualcalculation tecnnique Although applied In the example to a

dual repair types, the technique is

ypes. For 10rge number~ of repair types,

jjstenicomprised of only four indiv

applicable to ?ny r,umberof repair ‘

it wCLld be Ccni’eriertto use a programmable :~lcu!at~r with a norm~l

distribution program.

i~ij, Another practical calculation al~ernative for handling large numbers of

repair types with the manual calculation technique is by grouping the data. It

IS assumed the necessary Caiculatlons have Oeen made to obtain the MU “S~J

and all 2’s, or they are given directly. Group the ordered repair typen~

P.m, ‘s intO 1 time Intervals of length At. For each set of data a mst

suitable number, 1, of classes can be found. Sturges has developed the simple

rule 1 = 1+3.3 log,O N where 1 is the number of classes and N 1s the number

of data. ADDroximate the actual di$trtbutlon of repair type p~mj’s !n

each of the 1 time intervals by a normal distribution with a mean (p,)

calculated as th failure rate-we!ghted repair type mean

i 1p, = Zp. A.jlzl (10)

mJi

where Z indicates the sum is taken over the ii” interval and a variance

(U,2) calculated as the failure rate-weighted repair type variance

2 i~i

al -run L,lrl

n~

(11)

D-V-7

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, I-,I

I

1

!

I

(II

II

II I

II ,

fm-

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e

f.m

vGO

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r- 92. .

--

inNg

801-UI0

0“

u-edml

0.

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.u

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m.m

I I

12 Jan 1984

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MIL-HDBK-472

L

61BL10GRAPHY

1. Maintainability - Prediction: Theoretical Basis and Practical Approachof, USAF Aeronautical systems Division, 15 FeD 1962.

2, Maintainability - Prediction: Theoretical Basis and Practical Approachof, (JSAfAeronautical Systems Division, 31 Dec 1963.

3. Maintainability - Design Crlterla Handbook for Designers of ShipboardElectronic Equipment, NAVWIPS 94324, 30 Apr 1962.

4. A Research Plan for Developing Methods of Malntalnability Measurement andPrediction, Rome Air Development Center Tech. Note No. RADC-TN-60-5, AD-231090, 6 Jan 1960.

5. A Review of the Literature on Design of Information Job Performance Aids.Proj. No. 1710. USAF Airborne Systems Division Report No. ASDTR 61-549, 1961.

6. Maintainability Measurement and Prediction Methods for A.F. GroundElectronic Equipments, Phase 11 Report RADC-TN-61-141, AD-262 454, 15 Jun 1961.

7. Maintainability Measurement and Prediction Methods for A. F. GroundElectronic Equipments, Phase 11 Report RAOC-TN-60-221, AD-247 155. 15 Seo 1961.

8. Maintainability - Prediction Technique, Phase IV Report RADC-TDR-62-156,AD-277 199, 15 Mar 1962.

9. Malntainabillty Engineering, Phase V Report RADC-TDR-63-85,Vol. 2, AD-404898. 5 Feb 1963.

10. Malntalnbility Technique 5tudy, Final Technical Report, Phase V ReportRADC-TDR-63-85, Vol. 1 AO-404 899, 5 Feb 1963.

11. Maintainability and Supportabllty Evaluation Technique, Mright-AirDevelopment Division, Part I, Part II, Vo]s. 1 and 2, May and Jun 1960.

12. Malntainablllty Prediction and Analysts Study, Final Technical ReportRADC-TR-78-169, AD-A059753, Jul 1978.

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