Reliability Growth Testing (RGT) Plan

L o n g T e r m Q u a l i t y A s s u r a n c e ( L T Q A ) , h i l a i r e p e r e r a @ r o g e r s . c o m

Reliability Growth Testing (RGT) Plan

For

End Unit

Prepared by:

Hilaire Perera, P.Eng.


TABLE OF CONTENTS

Page No.

Purpose ---------------------------------------------------------------------------------- 3

Scope ---------------------------------------------------------------------------------- 3

Definitions ---------------------------------------------------------------------------------- 3

Responsibilities ----------------------------------------------------------------------------------- 3

Procedure

Selection of Growth Model ------------------------------------------------- 4

Duane Plot Example using Regression Analysis ------------------------- 4

Approximate Confidence Bounds for the MTBF ------------------------- 6 at the end of Duane Test

Reliability Growth Management -------------------------------------------- 7

Determination of Test Conditions ----------------------------------------- 7

Failure Reporting, Analysis and Corrective Action System ------------ 8

Steps in Creating the Duane Model Plot for Analysis ------------------- 9

Prediction of End Unit RGT Growth Time Using Growth Rate of 0.4-- 9

Reliability Growth Assessment --------------------------------------------- 10

Reliability Growth Success Criteria --------------------------------------- 10

ASSOCIATED DOCUMENTS MIL-STD-721: Definitions Of Terms For Reliability And Maintainability

MIL-HDBK-189: Reliability Growth Management

MIL-STD-1635: Reliability Growth Testing

MIL-HDBK-338B Electronic Reliability Design Handbook

NIST/SEMATECH Engineering Statistics Handbook


Reliability Growth Testing (RGT) Plan

Purpose RGT is a planned test-analyze-and-fix (TAAF) process in which End Unit is tested

under actual, simulated, or accelerated environments to disclose design deficiencies and defects. It is intended to provide a basis for early incorporation of corrective actions and for verification of their effectiveness, thus promoting reliability growth. RGT is intended to correct failures that reduce operational effectiveness and failures that increase maintenance and logistics support costs.

The formal test program dedicated to reliability growth should be deferred until after environmental qualification, when the design of the prototype or preproduction equipment which is to be used in RGT reflects the anticipated configuration and manufacturing processes to be used in production, but prior to commitment to production.

Scope Reliability Engineering Tasks in Growth Testing focus on the prevention, detection, and correction of reliability design deficiencies, weak parts, and workmanship defects. An effective reliability program stresses early investment in reliability engineering tasks to avoid subsequent additional costs and schedule delays. MTBF growth is not expected to increase indefinitely in time, in use no growth or negative growth may occur.

Definitions Mean Time Between Failure (MTBF) is a measure of reliability for repairable items: The mean number of hours during which all parts of the item perform within their specified limits, during a particular measurement interval under stated conditions

Corrective Maintenance (Repair). The actions performed as a result of failure to restore an item to a specified condition

Observed Mean Time Between Failure is equal to the total operating time of the equipment divided by the number of relevant failures

Predicted Mean Time Between Failure is that value determined by reliability prediction methods and is based on the equipment design and the use environment

Reliability Growth. The positive improvement of the reliability of equipment through the systematic and permanent removal of failure mechanisms

Responsibilities

It is the responsibility of the reliability engineer assigned to the particular project to prepare the RGT Plan, and together with a test engineer to prepare the RGT Test Procedure. These documents should be reviewed and approved by the Manager, Quality and Technical and the Project Manager


Procedure

Reliability Growth Testing (RGT) Plan Continued

Selection of the Growth Model

The approach to reliability growth is based on the Duane model. This model provides a deterministic approach to reliability growth. In this way the unit MTBF vs. Operating Hours falls along a straight line when plotted on ‘log-log’ paper That

is, the change in MTBF during development is proportional to T where T is the

cumulative operating time and is the rate of growth corresponding to the rapidity with which faults are found, and changes are made to permanently eliminate the basic causes of the faults observed.

This type of plot is called a Duane Plot and the slope of the best line through the points is called the reliability growth slope or Duane plot slope

Equation (1) is linearized by taking the “natural log” of both sides

LN (mc) = LN (b) + α LN (T) ------------ (2) mc = Cumulative MTBF T = Cumulative Test Time b = The cumulative mean time between failures at T = 1, the beginning of the “growth” work α = The slope of the straight line on the LN-LN plot Instantaneous MTBF (mi) = (1 / (1-α))mc

The parameters “b” and “α” can also be calculated by applying least squares (Linear Regression) analysis on equation (2) using EXCEL software

Duane Plot Example using Regression Analysis

The observed failure times used were: 5, 40, 43, 175, 389, 712, 747, 795, 1299 and 1478 hours, with the test ending at 1500 hours. After using this information in a regression analysis, the following parameters were calculated. (a) Growth Slope α; (b) MTBF at the end of test; (c) MTBF at 80% Confidence Interval; (d) MTBF at 90% Lower Confidence Limit

Duane Equation: mc = bTα ---------------- (1)



MTBF Data for Regression Analysis

Age (Hrs) Cum MTBF (Hrs) LN‐Age LN‐Cum MTBF

5 5 1.609437912 1.609437912

40 20 3.688879454 2.995732274

43 14.33333333 3.761200116 2.662587827

175 43.75 5.164785974 3.778491613

389 77.8 5.963579344 4.354141431

712 118.6666667 6.568077911 4.776318442

747 106.7142857 6.616065185 4.670155036

795 99.375 6.678342115 4.598900573

1299 144.3333333 7.169350017 4.972125439

1478 147.8 7.298445102 4.995860009

1500 150 7.313220387 5.010635294

Growth Slope = 0.61 Instantaneous MTBF at the end of 1500 Hour Test = 159/0.39 = 408 Hours ----- Use Eqn. (1) MTBF (MTBFlow = 288; MTBFhigh = 475) @ 80% Confidence Interval

MTBF = 288 @ 90% Lower Confidence Limit



Approximate Confidence Bounds for the MTBF at End of Duane Test

Confidence Level = 80%, Significance Level (α) = 20% Standard Normal Distribution result for significance α/2, for Two sided z 0.539827 MTBF 408 Hours Number of failures in the Growth Time r 10

mL MTBFr r 1( )[ ]

rz2

4 r

z2

2

z4

16

0.5

2

mL 288.483 MTBF Lower Bound

mU MTBFr r 1( )[ ]

r zr

2

.5

2

mU 474.939 MTBF Upper Bound

Confidence Level = 90%, Significance Level (α) = 10% Standard Normal Distribution result for significance α, for Single sided z 0.539827

mL MTBFr r 1( )[ ]

rz2

4 r

z2

2

z4

16

0.5

2

mL 288.483 MTBF Lower Bound

Note:

MTBF Upper & Lower Bounds are calculated

using the shown equations in “MATHCAD”

software program.

The “z” value is from “EXCEL” software

program, and if needed the required MTBF

values can be calculated using the equations in

“EXCEL”

Slope Calc.xls



Procedure (Continued) Reliability Growth Management

Reliability growth management is the systematic planning for reliability achievement as a function of time and other resources and is used for controlling the ongoing rate of achievement by reallocation of resources based on comparisons between planned and assessed reliability values. Reliability growth management is part of the system engineering process. It does not take the place of the other basic reliability program activities such as predictions, apportionment, failure mode and effect analysis, and stress analysis. Instead, reliability growth management provides a means of viewing all the reliability program activities in an integrated manner. It is imperative to recognize that a total reliability program is needed for effective reliability growth management.

Determining the Test Conditions

The initial step is the development of a representative Mission/Life Cycle Profile, by determining the most stressful environmental conditions and durations of stress that the system will experience during its life cycle.

For systems that have multiple missions and/or environmentally distinct mission phases, thorough environmental simulation in the RGT often is impractical. In these cases, the choice of mission(s), phase(s) or combined mission profiles to be simulated should be driven by the combination of operational relevance and feasibility of measurement. Almost always, the RGT combined environments should include temperature cycling and vibration as a minimum, along with operational stresses such as on/off cycling and variation in inputs (e.g. line voltage) and outputs (e.g. loads).

Rate of Growth is depicted by the slope of the growth curve. This, in turn, is governed by the amount of control, rigor, and efficiency by which failures are discovered, analyzed, and corrected through design and quality action. Test programs which foster the discovery of failures, coupled with management supported analysis and timely corrective action, will result in a faster growth rate and consequently less total test time.



Procedure Failure Reporting, Analysis and Corrective Action System (FRACAS) (continued)

A disciplined and aggressive closed-loop FRACAS is an essential element in the RGT process. The essence of a closed-loop FRACAS is that failures and faults of both hardware and software are formally reported, analysis is performed to determine failure cause, and positive corrective actions are identified, implemented, and verified to prevent further recurrence.

For a successful RGT process, all failures must be analyzed to the extent needed to determine the root cause of the failure. In many instances, this will not require a detailed laboratory analysis because the cause of the failure, such as test procedure errors, wrong parts, overstressed parts, workmanship errors, etc., will be readily apparent. Likewise, the corrective actions for many of these failure types will be relatively straightforward and easily implemented.

Early elimination of failure modes, and thus early implementation of a good FRACAS, has the following advantages:

• Cost and schedule savings. • Ample time to assess corrective actions.

• Reduction of previously identified failure modes; reducing redundant data analysis. • Adequate time to address all failures prior to full rate production (i.e.

prevention of corrective action backlog).

If RGT results are to be interpreted correctly, all test conditions and occurrences must be recorded accurately and completely. A solution and key complement to FRACAS is the test log because a major source of problems is the dynamic status of test item configurations. By definition, when reliability growth is taking place, the equipment is changing (normally both hardware and software). In addition, temporary repairs/replacements usually are permitted so that testing may continue while permanent fixes are being explored.


Reliability Growth Testing (RGT) Plan, Continued

Procedure (Continued)

Steps in Creating the Duane Model Plot (Page 11) for Analysis a. Using three cycle ln-ln paper, draw horizontal lines at the required MTBF

value and the predicted MTBF

b. Plot growth line start point at 100 test hours and 15% of predicted MTBF

c. The suitable range of reliability growth is represented by the Growth Rate α of 0.3 and 0.6. Draw a line representing Growth Rate α = 0.4. The selected Growth Rate line is considered the baseline against which reliability growth can be evaluated during the reliability growth test

d. Once 5 Failure/Time data points are obtained, determine Growth Slope α and draw the growth rate line. Continue test

e. The intersection of the selected growth rate line and the required MTBF line yields an approximation of total test time required

Prediction of End Unit Growth Time using Growth Rate of 0.4

The End Unit that has undergone environmental Stress Screening (ESS) [ESS

should be conducted on all electronic equipment scheduled for RGT. This helps

prevent overloading the RGT with problems not directly related to design] should be tested for the predicted Growth Time based on the following conditions..

Specified MTBF = 6000 Hours ______ Predicted MTBF = 12645 Hours _______ Preconditioning (Initial Test ) Time = 100 Hours

The End Unit undergoing RGT should assume to have the following characteristics:

(a) Assumed Growth Rate = 0.4 (Suitable Growth Rates are between 0.3 & 0.6) used as an aggressive reliability program is being followed

(b) A Starting point of 15% of the predicted MTBF for the cumulative MTBF Line

(c) A Starting point of 25% (100 * 0.15 / (1-)) of the predicted MTBF for the instantaneous MTBF Line

Duane Model

LN (Specified MTBF) - LN (0.15 of Predicted MTBF)

=

LN (Test Time = T) - LN (Preconditioning Time)


Reliability Growth Testing (RGT) Plan, Continued

LN (6000) – LN (1897)

0.4 =

LN (T) – LN (100)

8.70 – 7.55 0.4 =

LN (T) – 4.61

LN (T) = 2.875 + 4.61

T = e7.485

Reliability Growth Assessment

The reliability growth assessment should be obtained by calculating the Growth Rate α, using data from the tests. The reliability of the End Unit will be monitored by a Growth Plot (Cumulative MTBF vs Cumulative Test Time). The Instantaneous MTBF (Cumulative MTBF/ (1- α) ) plots should be included in periodic reports, according to Schedule requirements

Reliability Growth Test Success Criteria

The reliability growth test and its associated failure analysis and corrective action activity should be considered satisfactory if any of the following conditions exist:

The plotted MTBF values remain on or above the planned growth line

The best-fit straight line is congruent with or above the planned line

The best-fit straight line is below the planned line, but its slope is such that a projection of the line crosses the horizontal (Specified MTBF) line by the time the planned growth line reaches the same point

If none of the above conditions exist, it should be assumed that the planned reliability growth cannot be achieved with the current level of activity. Before a corrective action plan is determined, a careful analysis of the End Unit design and related failures should be made, to ascertain the problem areas and possible design modifications.

Predicted

RGT Time (T) = 1781 Hours


Reliability Growth Testing (RGT), Continued

Procedure (Continued)

.

The Instantaneous MTBF is the model mathematical representation of MTBF if

all previous failure occurrences are corrected

Instantaneous MTBF = (1 / (1 – α)) times Cumulative MTBF

15% of 12645

=1897

100

MTBF (predicted) =12645

MTBF (specified) =6000

MTB

F ‐ Hrs

Cumulative Test Time (T) ‐ HrsT=100

Total Test Time

Required

T = 1781

Planned

Cumulative MTBF

Growth Line has

α = 0.4

25% of 12645 =

3161

Planned Instantaneous

MTBF

Duane Model Plot

Reliability Growth Testing (RGT) Plan

Engineering

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