17022 Reliability

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Monday, 22 April 2013 LOVELY PROFESSIONAL UNIVERSITY By- H imanshu Gupta

RELIABILITY

DEFINITION

Reliability is the ability of an item to perform its intended function

under stated operation conditions for a given period of time. The definition stresses on four significant elements probability,

intended function, time and operating conditions.

Probability

Consideration of variation makes reliability a probability. It ispossible to identify the frequency distribution of an item, whichpermits prediction of life of the item, e.g., the probability of an itemfunctioning is 0.85 for 60 hours indicates that only 85 times out of100, we would expect the item to be functioning for a period of 60hours.

Intended Function

For an item to be reliable, it must perform a certain functionssatisfactorily when called upon to do.

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RELIABILITY

Time

Time is the most important factor in the assessment of reliability,since it represents a measure of period during which one can expecta certain degree of performance from an item.

Stated Conditions

The applications and operating circumstances under which an item isput to use is an important component of reliability. As the operatingconditions change, the reliability of an item also changes. Operatingconditions such as temperature, humidity, torque, and corrosive

atmosphere all have a definite effect on performance.

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RELIABILITY

Failure

Failure of an item represents unreliability. Thus, to compute the

reliability of an item, it is necessary to understand the concept offailure. A deviation in the properties of an item from the prescribedconditions is considered as fault. A state of fault is denoted asFailure.

An item is considered to have failed under one of the followingconditions:

When it becomes completely inoperable.

When it is still operable, but no longer able to perform a requiredfunction.

When a serious deterioration makes the item unsafe for its continued

use.

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RELIABILITY

Causes of Failure

Some of the causes of failures are:

Deficiencies in design.

Improper selection of process and manufacturing technique.

Lack of knowledge and experience.

Error of assembly.

Improper service conditions.

Inadequate maintenance.

Variation in environmental and operating conditions.

Human errors.

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RELIABILITY

Nature/Modes of Failures

The different modes of failure are:

1) Catastrophic Failures: In this case, a normally operating itemsuddenly becomes inoperative. Example: Blowing of a fuse orelectric bulb.

2) Degradation (Creeping) Failures: These failures occur graduallybecause of change in some parameter with time. Example, change inresistance will affect the performance of a resistor.

3) Independent Failures: These are the failures, which occurindependently and does not depend on failure of the others.

4) Secondary Failures: A secondary failure occurs as a result of someprimary failure. For example tsunami occurred due to earthquake.

5) Failure due to improper handling and misuse: These are causedmainly due to certain factors like overloading, stressing beyond thecapacity.

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Bath Tub Curve (Phases of Failures)

Analysis of failure data has shown that failures in general can begrouped into different modes depending upon the nature of thefailure. When a large number of units are put into operation, it islikely that there is a large number of failures initially. Thesefailures are called Initial failures or Infant Mortality.

After the initial failures, for a long period of time of operationfewer failures are reported but it is difficult to determine theircauses. The failures during this period are often called random orcatastrophic failures. This is a period of normal operation.

As the time passes, the units get worn out due to wear and tearand begin to deteriorate. Here in this period, the failures are dueto wear and tear and due to ageing. This region is called the wearout region.

This curve is also called as Life Cycle Curve.

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F

A

I

L

U

R

E

R

A

T

E

Time (hours, miles, cycles, etc)

EARLY LIFE

(burn-in or

break-in or

infant mortality

period)

(failure rate

decreases with time)

USEFUL LIFE

(or normal life)

(failure rate approx. const)

WEAROUT LIFE

(failure rate

increases with time)



Early Failures

These failures occur at the beginning due to the probability ofdefective design, manufacturing or assembly and qualitycontrol techniques during manufacturing.

These are eliminated by debugging or burn in process. The weakand substandard products/components that fail during early hoursof system operation are replaced by good or tested components.Debugging is a method of accelerating the completion of earlyfailures by operating the system continuously for number ofhours, correcting them and then releasing the system for actualuse.

Debugging is done generally prior to dispatch to the user toensure the detection and elimination of early failures.

Warranty is based on the concept of early failures.

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Catastrophic (Chance) Failures

These failures are predominant during actual working of the

system. They occur randomly and unexpectedly. The failure rate is fairly constant. These are caused due to sudden

stress accumulation beyond the design strength of the material.

This phase is called the useful life of the component. The failuresat this stage can be minimised by introducing redundancy in thesystem.

Wear Out Failures

The item is more likely to fail due to wear and tear and thenumber of failures will be high.

This is a typical ageing problem. Proper care and maintenancewill reduce the failures at this stage.

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Measures of Reliability/ Quantification of Reliability

1) Failure Rate

Failure rate is expressed in terms of failures per unit time i.e. asfailures per hour, or failures per 100 or 1000 hours. Failure rate isthe ratio of number of failures (f) during a specified test intervalto the total test time of items undergoing test.

= f/T

= Failure rate

f = Number of failures during the test interval

T= Total test time When the design is new, failure rate is high and when the design

is matured, the failure rate is fairly constant. Smaller the value offailure rate, higher is the reliability of the system.

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Measures of Reliability

2) Mean Time Between Failures (MTBF)

MTBF is referred to as the average time of satisfactory operation

of the system. Larger the MTBF, higher is the reliability of thesystem. It is applicable to repairable systems and is expressed inhours, e.g. If an item fails 8 times over a period of 40,000 hoursof operation, the MTBF would be 500 hours. During the operatingperiod, the failure rate is fairly constant.

MTBF is the reciprocal of the constant failure rate or the ratio oftest time to number of failures.

MTBF = 1/

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Measures of Reliability

3) Mean Time To Failures (MTTF)

This is applicable to non-repair systems. The mean time to failureis expressed as the average time an item is expected to functionbefore failure. If we have the life test information on n itemswith failure times t1, t2,.tn, then the mean time to failure isdefined as

MTTF = 1/nti, where i= 1 to n

The exponential formula for ReliabilityThe distribution of time between failures indicates the chance of a

failure-free operation for a specific time interval. When thefailure rate is constant, the probability of survival (reliability) isgiven by:

Ps = R = e-t

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System Reliability

System

A system is a collection of components, subsystem and/or assemblies

arranged to a specific design order to achieve desired functions with

acceptable performance and reliability.

Overall system results in the functioning of a product and a measure

of how well a system performs are based on the quality of design. The

basic steps for establishing system reliability are as follows:

The components and sub-systems constituting a given system and individual

reliability factors can be estimated, identified and computed.

A block diagram known as reliability block diagram represents the

configuration of a systems sub-components.

The condition for a successful operation of a system is then established todecide the functioning of components.

Combination rules of theory of probability are formulated to estimate a systems

reliability.

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System Reliability

Types of a System

Repairable System

It is a system that can be restored to an operating condition after a

failure by a repair or replacement of one or more components. The

following are the types of reparable systems:

Continuously Operating System: This type of system, when put in

operation to function, continues to operate till its failure or it stops for

planned maintenance schedules. For example, nuclear reactors or

satellites. On and off Operating System: Such a system can be operated at the

time when a consumer desires, and it can be re-operated when required,

for example, television, mobile phones.

Intermittently Operating System: This type of system is always ready

to perform but is operating intermittently, for example, cars and planes.

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System Reliability

Types of a System

Non Repairable System

It is also known as an instantaneous operating system with only one

cycle of performance, for example, fuses and flash bulbs.

Reliability Block Diagram

It is a diagram that represents how the components of a product,

represented by blocks, are arranged and related reliability-wise in a

larger system. It is often, but not necessarily, same as the way thatcomponents are physically related.

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System Reliability

System

A system is a collection of components, subsystem and/or assemblies

arranged to a specific design order to achieve desired functions with

acceptable performance and reliability.

Models of a System

Series Structure

For this system to work, both components 1 and 2 must work.

In this case, all n components must work in order for the whole

system to work.

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1 2

1 2 . . . n


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System Reliability

A Personal Computer

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Power

Supply

Motherboard ProcessorHard

Drive

A Simple Series system

Parallel Structures

1

2

1

2

.

.

.

n


System Reliability

In a parallel system, the system will work as long as at least one

component works.

Combination of Series and Parallel Structures

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1 2

3


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System Reliability

Finding A Systems Reliability

A) A Series System

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1 2 n. . .

For a pure series system, the system reliability is equal to the

product of the reliabilities of its constituent components. Or:

ns

RRRR ...21


System Reliability


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B) A Parallel System

1

2

n

..

.

For a pure parallel system, the overall

system reliability is equal to the product

of the component unreliability's.

Thus, the reliability of the parallel

system is given by:

Rs = 1 [(1 R1)(1-R2)(1-Rn)]


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System Reliability


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C) Combination of Series and Parallel Structures

Example:Consider a system with three components. Units 1 and 2 are connected

in series and Unit 3 is connected in parallel with the first two, as shown

in the figure below. Find the reliability of the system.

Solution:

R1

= 0.99 R2= 0.98

R3 = 0.97


System Reliability


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First, the reliability of the segment consisting of Units 1 and 2 is

calculated:

R1,2 = (R1)(R2)

= (0.99)(0.98)

= 0.97

The reliability of the overall system is then calculated by treating Units

1 and 2 as one with a reliability of 0.97 connected in parallel with Unit3.

Therefore: R1,2= 0.97

R3 = 0.97

Rs = 1 [(1 0.97)(1 0.97)]

= 0.9991

= 99.91%


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System Reliability


Bridge System

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A bridge system is a combination of all types of redundancies, and it is customized tomeet particular requirements. An inspection of this system reveals that any of the

following failures will cause the system to fail: failure of components 1 and 2, failures

of components 3 and 4, failure of components 1 and 5 and 4, and failure of components

2 and 5 and 3.

1 3

2

5

4


System Reliability


Standby Redundancy

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In a standby redundancy, only one component is operating where one or

more components are in a standby mode to take over the operation, if the

already operating component fails without accumulating any time. In

case of parallel network, all the units in the configuration are active,

whereas in standby redundancy, they are not.

Reliability of a standby redundancy of n units in which one unit is

operating and n-1 units are standby, ready to take over, until operatingunit fails, is given by

Rst (t) = (t)re t/ r!

r= 1

n-1


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Reliability Improvement

A high degree of reliability is an absolute necessity for complexand modern systems to be used for industrial, military and other

scientific purposes. There are many ways by which reliability of acomponent or system can be enhanced. These are:

1) Design and Safety Factor: In order to design reliability intoproducts, reasons for product failures must be analyzedthoroughly. Generally, a product fails prematurely because ofinadequate design features, manufacturing and part defects,abnormal stresses induced, environmental condition and humanerror. Higher reliability could be achieved through mature design.

2) Parts and Material Selection: Designer has to choose betweenselecting standard parts and manufactured specialized parts with

higher reliability and greater tolerances. The trade off is usually incost but ease of parts availability, ease of repair, energyrequirements, weight and size may also be considered.

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Reliability Improvement

3) Redundancy: When it is not possible either to manufacture ahighly reliable component or the cost associated with suchmanufacturing is too high, the system reliability can be improvedby the techniques of redundancy.

Redundancy is the duplication of critical components or functionsof a system with the intention of increasing reliability of thesystem.

The various approaches of introducing redundancy in thesystem are:

a) To provide a duplicate or an additional path for the entire systemitself. This is known as system or unit redundancy.

b) To provide redundant path for each component individuallywhich is called component redundancy.

c) Use a combination of the above methods depending upon theconfiguration called mixed redundancy.

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Failure Analysis

Failure analysis techniques provide a methodical way to examine aproposed design for possible ways in which a failure can occur.There are two ways by which a failure analysis is done in reliabilityengineering:

1. Failure Mode and Effect Analysis (FMEA)/ Failure Mode andEffect Criticality Analysis (FMECA).

2. Fault Tree Analysis (FTA).

Fault Tree Analysis

The FTA is one of the many symbolic analytical logic techniquesfound in operations research and system reliability. Fault treediagrams are logic block diagrams that display state of system (top

event) in terms of the states of its components (basic events). FTDsprovide an alternative to RBDs. An FTD is built top-down in termsof events rather than blocks.

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System Safety and Fault Tree Analysis

Reliability and product safety are obviously related. Safety can bebroadly defined as the avoidance of conditions that can causeinjury, loss of life, or severe damage. Therefore the focus here ison failures that may create safety hazards.

The objective is to determine during design how these failures arelikely to occur, to estimate their probability of occurrence, and totake corrective action.

Fault Tree Analysis

A useful tool in performing a system safety analysis.

It is a graphical design technique that provides an alternative toreliability block diagrams.

It is a top-down, deductive analysis structured in terms of eventsrather than components. The perspective is on faults rather thanreliability.

All failures are faults, but not all faults may be consideredfailures.

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Fault Tree Analysis

There are four major steps to a fault tree analysis:

i. Define the system, its boundaries, and the top event.ii. Construct the fault tree, which symbolically represents the system

and its relevant events.

iii. Perform a qualitative evaluation by identifying thosecombinations of events that will cause the top event.

iv. Perform a quantitative evaluation by assigning failureprobabilities or unavailability's to the basic events and computingthe probability of the top event.

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Fault tree main symbols

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Commonly Used Symbols Occasionally Used Symbols

OR gate Incomplete event

AND gate An External Event

An Event / Fault gate

Basic Event


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FTA Symbols Explained

Basic Event: A lower most event that can not be further developed.E.g. Relay failure, Switch failure etc.,

An Event / Fault: This can be a intermediate event (or) a top event. Theyare a result logical combination of lower level events.

E.g. Both transmitters fail, Run away reaction

OR Gate: Either one of the bottom event results in occurrence of the top event.

E.g. Either one of the root valve is closed, process signal to transmitter fails.

AND Gate: For the top event to occur all the bottom events shouldoccur.

E.g. Fuel, Oxygen and Ignition source has to be present for fire.



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FTA Symbols Explained

Incomplete Event: An event which has scope for further development butnot done usually because of insufficient data.

E.g. Software malfunction, Human Error etc.,

External Event: An event external to the system which can cause failure.E.g. Fire.


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Simple Examples

Example 1:

Example 2:

Transmitter Failed

OR

Transmitter 1

Failed

Transmitter 2

Failed

Valve Failed

Valve 1

Failed

Valve 2

Failed

AND

0.1 0.2

0.28

0.001 0.002



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Procedure

Steps to get the final Boolean equation:

1. Replace AND gates with the product of their inputs.

IE1 = A.B

IE2 = C.D

2. Replace OR gates with the sum of their inputs.

TOP = IE1+IE2

= A.B+C.D

3. Continue this replacement until all intermediate event gates

have been replaced and only the basic events remain in the

equation.

TOP = A.B+C.D

TOP

IE1 IE2

A B C D


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Procedure

Boolean Algebra Reduction Example:TOP = IE1 + IE2

= (A.B) + (A + IE3)

= A.B + A + (C.D.IE4)

= A.B + A + (C.D.D.B)

= A + A.B + B.C.D.D (D.D = D)

= A + A.B + B.C.D (A + A.B = A)

= A + B.C.D A B A IE3

C DIE4

D B

TOP

IE1 IE2



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Faults can be classified as primary, secondary, and command.

A fault is primary if the component or part is functioning withinits design parameters when an inherent failure occurs.

A secondary failure occurs when an environmental stress or anexcessive operational stress causes the failure.

A command fault is one that occurs as a result of a correct actionbeing accomplished at a wrong time or place.

For example, a command fault may occur when turning power onprematurely or turning off a cooling subsystem before the systemhas been shut down.


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Failure Mode Effect and Criticality Analysis (FMECA)

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What Is A Failure Mode?

A Failure Mode is: The way in which the component, subassembly, product,

input, or process could fail to perform its intended

function.

Failure modes may be the result of upstream operations or

may cause downstream operations to fail

Things that could go wrong


Failure Mode Effect and Criticality Analysis

(FMECA)/FMEA

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FMEA

A structured approach to:

Identifying the ways in which a product or process can

fail

Estimating risk associated with specific causes

Prioritizing the actions that should be taken to reduce

risk

Evaluating design validation plan (design FMEA) orcurrent control plan (process FMEA)


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(FMECA)/FMEA

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The FMEA Form

Identify failure modes

and their effectsIdentify causes of the

failure modes

and controls

PrioritizeDetermine and assess

actions



(FMECA)/FMEA

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Types of FMEAs

Design Analyzes product design before release to production,

with a focus on product function Analyzes systems and subsystems in early concept and

design stages

Process Used to analyze manufacturing and assembly processes

after they are implemented


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(FMECA)/FMEA

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FMEA Procedure

1. For each process input (start with high value inputs),determine the ways in which the input can go wrong

(failure mode)

2. For each failure mode, determine effects

Select a severity level for each effect

3. Identify potential causes of each failure mode

Select an occurrence level for each cause

4. List current controls for each cause

Select a detection level for each cause



(FMECA)/FMEA

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FMEA Procedure

5. Calculate the Risk Priority Number (RPN)

6. Develop recommended actions, assign responsible persons,

and take actions

Give priority to high RPNs

MUST look at severities rated a 10

7. Assign the predicted severity, occurrence, and detectionlevels and compare RPNs


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(FMECA)/FMEA

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Severity, Occurrence, and Detection

SeverityImportance of the effect on customer requirements

Occurrence

Frequency with which a given cause occurs and

creates failure modes

Detection

The ability of the current control scheme to detect

or prevent a given cause



(FMECA)/FMEA

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Rating Scales

Severity

1 = Not Severe, 10 = Very Severe

Occurrence

1 = Not Likely, 10 = Very Likely

Detection

1 = Easy to Detect, 10 = Not easy to Detect


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(FMECA)/FMEA

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Risk Priority Number (RPN)

RPN is the product of the severity, occurrence, and

detection scores.

Severity Occurrence Detection RPNX X =


Acceptance Sampling Plan based on Life test

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A common life testing plan involves choosing a sample of items

from the batch and observing their operation for a certain

predetermined time. If the number of failures exceeds a stipulated

acceptance number, the lot is rejected; if the number of failures is

less than or equal to the acceptance number, the lot is accepted.

Two options are possible. In the first option, an item that fails is

replaced immediately by an identical item. In the second, failed

items are not replaced.

In calculations for OC curve both Poisson and Binomial

distributions can be used. The OC curve shows the probability of

lot acceptance Pa, as a function of lot quality as indicated by the

mean life () or the mean time to failure of the item.

Operating Characteristic Curves


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Acceptance Sampling Plan based on Life test

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The risk of rejecting a good lot (products with a satisfactory mean

life 0) is the producers risk.

The risk of accepting a poor lot (products with an unsatisfactory

mean life of1) is the consumers risk.

Operating Characteristic Curves


Reliability and Life Testing Plans

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Plans for reliability and life testing are usually destructive in nature.

They involve observing a sample of items until a certain number of

failures, observing over a certain period of time to record the number

of failures, or a combination of both. This testing is usually done at the

prototype stage, which can be expensive depending upon the unit cost

of the item.

Types of Tests

Three main types of tests

Failure Terminated Tests: In failure terminated plans, the tests are

terminated when a pre assigned number of failures occurs in the

chosen sample. Lot accepetance is based on the accumulated test time

of the items when the test is terminated.

Let predetermined number of failures be r, and the stipulated mean life

by C. From the test results, lets suppose the accumulated test time of

the items is T, from which the estimate of average life is,


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Failure Terminated Tests:

= T/r

If C lot is accepted.

Time Terminated Test:

A time terminated test is terminated when a preassigned time T is

reached. Acceptance of the lot is based on the observed number of

failures r` exceeds a preassigned value r, the lot is rejected, otherwise,

the lot is accepted.



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Sequential Reliability Testing:

In sequential reliability testing, no prior decision is made as to the

number of failures or the time to conduct the test. Instead the

accumulated results of the test are used to decide whether to accept the

lot, reject the lot, or continue testing.


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The cumulative number of failures based on the choice of the sampleis plotted versus, the accumulated test time of the items. Based on the

acceptable mean life 0, an associated producers risk , a minimum

mean life 1, and an associated consumer risk , equations for the

acceptance line and rejection line are found.

If the plot stays within the two lines, testing continues; if the plot falls

in acceptance region, the test is terminated and lot accepted; if the plot

falls in rejection region, the test is terminated and lot rejected.



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The cumulative number of failures based on the choice of the sample

is plotted versus, the accumulated test time of the items. Based on the

acceptable mean life 0, an associated producers risk , a minimum

mean life 1, and an associated consumer risk, equations for the

acceptance line and rejection line are found.

If the plot stays within the two lines, testing continues; if the plot falls

in acceptance region, the test is terminated and lot accepted; if the plot

falls in rejection region, the test is terminated and lot rejected.


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Availability

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An availability is a probability that a component/system is operational

at a given time, t (i.e. has not failed or been restored after failure).

The availability of an item is a probability that it is operatingsatisfactorily at any point of time, used in stated conditions including

an operating time, active repair time and logistic time.

If a vehicle has 99.9% availability, there is one time out of thousand

that someone needs to use the vehicle and finds out that the vehicle is

not operational because some part of the vehicle is either damaged or

in the process of being replaced.


Maintainability

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Maintainability is defined as the probability of performing a successful

repair action within a given time.

It is a measure of ease and speed with which a system can be restored

to operational status after a failure occurs.

M(t) = 1- e-ut

Where u is the repair rate

MTTR (Mean Time To Repair) = 1/u

17022 Reliability

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