1. Accelerated Testing - Chapter 1.pdf

8/10/2019 1. Accelerated Testing - Chapter 1.pdf

1/28

Accelerated

Testing

A

Practitioners Guide to

i^ated andReliabilityTesting

HarrySchwa

N.Cham. 62D647a

Autor:Dodson, Bryan, 1962-

Titulo:Accelerated testing : a practi

III


2/28

ACCELERATEDTESTING

A

Practitioner

Guide to

Accelerated andReliabilityTesting

BryanDodson

H a r r y

Schwab

SAE

nternational

Warrendale,

Pa.


3/28

Other SAE titles of interest:

Automotive Engineering Fundamentals

B y Richard

Stone

and Jeffrey K. B a l l

(Order No. R-199)

Finite Element Analysis for Design Engineers

B y

Paul M .

Kurowski

(Order No. R-349)

Finite

Elements: Their Design and Performance

B y

Richard H. MacNeal

(Order

No.

B-608)

An Introduction to Modern Vehicle Design

B y

Julian Happian-Smith

(Order No. R-295)

The System Integration Process for Accelerated

Development

B y

R.J. Menne and

M . N . Rechs

(Order No. R-319)

For more informationor to order a book, contact SAE International at

400 Commonwealth

Drive,

Warrendale, PA 15096-0001;

phone (724) 776-4970; fax (724) 776-0790;

e-mail [email protected];

website

http://store.sae.org.
mailto:[email protected]://store.sae.org/http://store.sae.org/mailto:[email protected]


4/28

A l lrights reserved. No part of this

publication

may be reproduced, stored in a

retrieval

system,

or

transmitted, in any

fo rm

or by any

means,

electronic, mechanical, photocopying, recording,

or

otherwise,withouttheprior

written

permission of SAE.

For

permission and licensing

requests,

contact:

SAE Permissions

400 Commonwealth

Drive

Warrendale, PA 15096-0001 USA

E-mail:

[email protected]

Tel :

724-772-4028

Fax: 724-772-4891

L i b r a r y

of Congress Cataloging-in-Publication Data

Dodson, Bryan, 1962-

Accelerated testing : a practitioner's guide to accelerated and

re l iabi l

i ty

testing / Bryan Dodson, Harry Schwab,

p. cm.

Includes

bibliographicalreferences

and index.

ISB-10 0-7680-0690-2

ISBN-13 978-0-7680-0690-2

1.Reliability

(Engineering).

I

Schwab, Harry. I I

Ti t le .

TS173.D612006

620'.00452dc22

2005057538

SAE

International

400 Commonwealth

Drive

Warrendale, PA 15096-0001 USA

E-mail:

[email protected]

Tel :

877

:

606-7323 (inside USA and

Canada)

724-776-4970 (outside USA)

Fax: 724-776-1615

0 \

Copyright2006

S A E

International

ISBN-100-7680-0690-2

ISBN-13

978-0-7680-0690-2

S A E

Order

No. R-304

Printed

in the United States of

America.
mailto:[email protected]:[email protected]:[email protected]:[email protected]


5/28

A C K N O W L E D G M E N T S

We are grateful to many individuals for helping

prepare

this book. Most notable are the review

ers. Several reviewers were anonymous, but you know who you are, and we thank you for your

comments. Special thanks go to Lois Dodson and Matthew Dodson for creating the web site

on

the accompanying CD. We greatly appreciate Thermotron for

providing

the ESS material in

Chapter 8, and the Quality Council of Indiana forallowingus to usesomepreviously published

materialin

Chapters

2 and 3.


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P R E F A C E

This

book

presentsaccelerated

testing

f rom

a practical viewpoint. The material is

presented

w i t h

the practitioner in

mind;

thus, proofs and derivations

have been

omitted, and

numerous

examples

have been

included. In addition, most examples

have been

worked in Microsof t

Excel

and are included in the accompanying CD. For those desiring proofs and derivations,

references

are provided. Our goal is that practicing

engineers w i l l

be

able

to apply the

methods

presented

after studying this text.

Practitioners

w i l l f ind

this text valuable as a comprehensive

reference

book, but this book is

also

ideal for use in college

courses.

In particular, it is recommended that this text be

used

for

one-semestercollege

courses. Students

should

have

a f ami l i ar i ty w i t h

basic

probability and

statistics before attempting this material.

The text consistsof eight chapters. Chapter1 provides an introduction and overview of the

limitationsof

accelerated

testing.

Chapters

2, 3, and 4

describe

the fundamentals of statistical

distributions,

the most commonly

used

distributions in

accelerated

testing, and

parameter

estima

t ionmethods. Chapter5

describes test

plansforacceleratedtesting,

including

r e l i abi l i ty growth.

Chapter

6 explains models for

accelerated

aging, along

w i t h

qualitative

methods

of

accelerated

testing.

Chapter

7 explains environmental

stress

screening (ESS), and

Chapter

8

presents

the

equipment andmethods usedinacceleratedtesting.

Besure to use the accompanying CD,

which

contains a website to organize the material. The

C D contains the f o l l o w i n g content:

Examples

Theexamples

presented

in the text are worked in Microsoft Excel templates.

Thesetemplates w i l l

be useful when applying the material to real-world problems.

Statistical Tables

The statistical

tables

included in the

appendices

of books are holdovers

to times when computers were not available.

These

tables

give solutions to closed integrals

of

functions that could not be solved

imp l i c i t ly

and required numerical

methods

to solve.

These

functions are now included in electronic

spreadsheets.

When the text

references

a

value available in Appendix A, use the Microsoft Exceltemplatesincluded on the CD.

B u r n I n

Optimization

This is a Microsoft Excel template for determining the optimum

burn-indurationbasedon the

cost

of burn-in time, burn-in failures, and

field

failures.

Random Number Generator

This Microsoft Excel template

generates

random

numbers

that can be used for simulations. There are random number

generators

for the Weibu l l ,

normal,

lognormal, and exponential distributions.


7/28

ACCELERATED TESTING

GovernmentDocuments

Thispagecontains many documents in PDF format. There are

numerous

military standards

and handbooks related to

reliability

and accelerated testing.

AMSAA Reliability

Growth Handbook

This pageprovides theAMSAA Reliability Growth

Handbook

inMicrosoft

Word

format.


8/28

C O N T E N T S

Chapter 1Introduction 1

ThePurposeof Accelerated Testing 1

Design L i f e 2

StatisticalSample SizeDetermination 5

Tolerancesin Accelerated Testing 5

Financial

Considerations

9

Summary 17

Chapter 2Probability Fundamentals 19

Sampling 19

Probability Density Function 21

Cumulative Distribution Function 25

Reliability

Function 27

Hazard Function 27

Expectation 29

Summary 31

Chapter 3Distributions 33

ContinuousModeling Distributions 33

Weibull

Distribution 33

Normal Distribution 39

Lognormal Distribution 46

Exponential Distribution 50

DiscreteModeling Distributions 55

PoissonDistribution 55

Binomial

Distribution 56

Hypergeometric Distribution 58

Geometric

Distribution 60

Identifying the Correct DiscreteDistribution < 61

- i x -


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ACCELERATED

TESTING

Sampling Distributions 61

Chi-SquareDistribution 62

f-Distribution

64

F-Distribution 66

Bayes'

Theorem 68

Summary 71

Chapter4

-ParameterEstimation 73

Maximum Likelihood Estimation 73

Probability Plotting 74

Hazard Plotting 74



Hazard Plotting 79


Normal Distribution 83


Hazard Plotting 87


Lognormal Distribution 91

WeibullDistribution 92


Hazard Plotting 95


Nonparametric ConfidenceIntervals 99

Summary 102

Chapter5Accelerated

TestPlans 103

Mean Time to Fail 103

TestPlanProblems 103

Zero-Failure Testing 109

Bogey Testing 109

Bayesian

Testing 110

Sequential

Testing 119

Pass-FailTesting 119


- x -


10/28

CONTENTS

Weibull

Distribution 126

Randomization of Load Cycles 131

Reliability

Growth 134

Reliability

Growth

Process

135

Reliability Growth Models 136

Summary 140

Chapter

6

Accelerated Testing Models 141

Linear Acceleration 141

Field

Correlation 142

Arrhenius Model 149

Eyring

Model 157

Voltage Models 169

Mechanical Crack Growth 170

Degradation Testing 171

Qualitative

Tests

176

Step-StressTesting 177

Elephant

Tests

179

H A L T and HASS 179

Summary 180

Chapter

7

EnvironmentalStressScreening 181

StressScreening Theory 181

The Product ReliabilityEquation 181

What Is

ESS?

184

The Evolution of ESS 184

Misconceptions About ESS 186

Types of EnvironmentalStress 187

AdvantagesofTemperatureCycling 193

Levels ofScreenComplexity 195

Failure Analysis 196

Case

Histories 197

Implementing an ESS Program 198

Equipment

.

...m-200-

Burn-InOptimization 202

Summary 205

- x i -


11/28

ACCELERATED TESTING

Chapter8TestEquipment Methods and Applications 20'

SimulationVersus Stimulation 20

Simulation 20

Stimulation

21

Types ofStresses 21'.

Temperature 2L

Vibration

2U

ElectricalStress

21

1

Combined Environments 211

Other Types of

Stress

21

1

Summary 21^

Appendix AStatisticalTables 221

TableA . 1 : The Gamma Function 221

TableA . 2 : Standard Normal CumulativeDistributionFunction 22/

Table

A . 3 :

Chi-Square Significance

224

TableA . 4 : F Significance 22t

Table

A . 5 : t

Significance 22S

Table

A . 6 :

Poisson Cumulative

Distribution

Function 225

Appendix B

Government Documents 231

Appendix CGlossary 233

AppendixD

List

of

Acronyms

243

References 247

Index 249

About the Authors 255

- x i i -


12/28


13/28


14/28


15/28

ACCELERATED TESTING

Asshown in Figure 1.2, the number of brake applicationsincreasesdramatically as the percent

o f the population covered

nears

100%. This istypicalof many other applications, such as door

slams, i gn i t ion cycles, andtrunkreleasecycles. To increase the percent of thepopulationcovered

f rom75% to 99.9 % requires an approximate

doubling

of the number of cycles in the accelerated

test. Notonlydoesthis increase the cost and duration of the test, but the cost of the component

increasesbecause

the number of cycles in the test is part of the design requirement.

The percent of the population covered is a compromise among development cost, development

time,

component cost, and the

field

performance of the component. For

safety-critical

items, the

userpercentile may exceed 100% toallowa safety margin. For other items, such as glove box

latches, theuserpercentile may be as low as 80%. Inreality,there is no 95th percentileuser.

There is a 95th percentileuserfor number of cycles, a 95th percentileuser for temperature, a

95thpercentileuserfor number of salt exposure, a 95th percentileuserforvibration,and so forth .

However,

determining the 95th percentileuserfor the combination of conditions is unrealistic.

The worst-case userprofilemay not be at thehighend for the number of cycles of operation.

Consider a parking brake. The worstcasemay be a brake that is used for the firsttime after the

vehicle

is 10

years

old. This type ofuserprofilemust be incorporatedintoa test

separate

f rom

a test u t i l i z i ng the 95th percentile ofparkingbrake applications.

- 4 -


16/28

INTRODUCTION

Accelerating

a test by

eliminating

the time between cycles can introduce unrealistic conditions.

Consider adurabilitytest for an automobile door. The door is opened and closed 38,000 times

in

12 hours. Opening and closing the door thisquickly

does

notallowthe door hinges or latches

tocool,nor

does

it give any contaminants that may be introduced in the hinges time to f o rm

corrosion. Consider an automobile engine: the 95th percentile

user

profile

for engine on-time is

approximately7,000 hours. Does running the engine for 7,000 consecutive hours approximate

7,000 hours ofoperationover 10years?Consider an automobile starter: the 95th percentileuser

profile

for the number of engine

starts

is approximately 4,000. Starting the engine 4,000 times

asquicklyas possible

does

notstressthe starter as much as actualusageconditions

because

the

engine

would

be warm for nearly every engine start. To more adequately represent true

usage

conditions,

the enginewouldneed to be cooled forsomeof the starts.

Statistical

Sample Size Determination

1

The sample sizesgiven in Table 1.1 are

based

on statistical sampling. Statistical confidence

ig assumesa random sample representative of the

population.

Obtaininga random sample represen

ts Q tative of the population requires allsourcesof

variation

to be present, such as the

f o l l o wi n g :

>

C

00

Variation f rom multipleproduction operators

Variation

f rom

multiplelots of raw materials

Variation f rom toolwear

Variation f rom machine maintenance

Variation f rom seasonalclimaticchanges

Variation f rom supplierchanges

It may be possible to obtain a random sample representative of the population for periodic

requalifications,

but it is nearly impossible for new product development. Thus, designing

tests

to

demonstrate r e l i abi l i ty w i t h statistical confidence is not always possible. Thebestalternative

is

to test w i t h worst-case tolerances.

TolerancesinAccelerated Testing

Determining the worst-case combination of tolerances can be d i f f icul t . Consider the simple

system shown in Figure 1.3. Component A is inserted

into

Component B and rotates during

operation. The worst-case tolerance is either Component A atmaximumdiameter and the inner

diameter of Component B at aminimum,or Component A at aminimumdiameter and the inner

diameter of Component B at a maximum.

Butevenw i t h this simple system, other tolerances must be accounted for, such as the

fo l lowing :

Surface finish (for both components)

Volume oflubricant

Viscosityoflubricant

Roundness (for both components)

Hardness (for both components)

- 5-


17/28

ACCELERATED TESTING

C o m p o n e n t

A

C o m p o n e n t

B

Figure

1.3 Simple tolerancing example.

The number of tolerance combinations can become unmanageable. Table 1.3 shows the

number of possible tolerance combinations as a function of the number of dimensions. W i t h

10 characteristics to consider for

worst-case

tolerancing in this simple two-component system,

there

are more than 1,000 combinations of

tolerances

to consider. Determining

which

ofthese

1,000 combinations is the worst

case

is often

difficult .

T A B L E 1

.3

N U M B E R OFT O L E R A N C E C O M B I N A T I O N S

Numberof Numberof

C h a r a c t e r i s t i c s T o l e r a n c e C o m b i n a t i o n s

2 4

3

8

4 16

5 32

10 1,024

20 1 048 576

50

1.126

( 1 0

1 5

)

100

1.268

( 1 0

3 0

)

Confounding

the problem is the fact that the worst-casetolerance combination for a specific

environmental condition may be the

best-case

tolerance combination for another environ

mental condit ion. Manufacturing capabilities

also

complicate testing at

worst-case

tolerance

- 6 -


18/28

INTRODUCTION

combinations. It isoftenimpossible orprohibitivelyexpensive to produce parts at the desired

tolerancelevel. In

these

cases,a compromise is made by using a dimension as close as possible

tothe desired value.

Ideally,

i f

al l

characteristics are w i t h i n tolerance, the systemwould workperfectly and survive

for the designed l i fe . And i fone or more characteristics are out of tolerance, the systemwould

fai l .

Reality demonstrates that a component w i t h a characteristic

slightly

out of tolerance is

nearlyidentical

to a component

w i t h

the

same

characteristic

slightly

w i t h i n tolerance. Toler

ances are not always scientifically determinedbecausetime and budget do not always allow

for

enough research. There is a strongcorrelationbetween the defect rate in the manufacturing

facil i ty and field r e l i abi l i ty . A

portion

of the reduction in defect rate has been due to a reduc

t ion

of manufacturing

variability.

As manufacturing

variability

is reduced, characteristics are

grouped

closer to the target.

Consider a motor

w i t h

its long-term

durability

dependent on the precision fit of three compo

nentsin ahousing. The three components are stacked in the housing;historically,the tolerance

stackup has

caused

durabilityproblems, and themaximumstackup of the three components has

been specified at 110. To meet this requirement, an engineer created the specifications shown

inTable 1.4.

T A B L E 1 4

MOTOR

C O M P O N E N T T O L E R A N C E S

C o m p o n e n t

A B C

Total

TargetSize

30

20

10

60

M a x i m u mSize 50 30 15

95

I fthe three components are manufactured to the target, thetotalstackup is 60. However, there

is always variance inprocesses, so the engineer specifies amaximum allowable size. I f the

manufacturing

capability for each of the components is 3 sigma (a defect rate of 67,000 parts

per

m i l l i on ) ,

the

process

w i l l produce the results shown in Figure 1.4 for the stackup of the

system.

By

increasing the manufacturing capability for each of the components to 4 sigma (a defect

rate of 6,200 parts per

m i l l i o n ) ,

the

process

w i l lproduce the results shown in Figure 1.5 for the

stackup of the system.

The

motor housing has a perfect fit w i t h the three components i f the stackup is 60. Any devia

t ion f rom 60

w i l l

reduce the l ifeof the motor. As

long

as the

total

stackup is

less

than 110, the

motor

w i l lhave an acceptable l i fe ;however, motorsw i t h a stackup closer to 60w i l llast longer.

I t is

easy

to see that the reduced variance in manufacturingw i l l increase the l i fe of the motors.

Manufacturing capability cannot be overlooked by r e l i abi l i ty engineers. First-time capability

verification,

statistical

process

control

(SPC), and

control

plans are essential toproviding highly

reliableproducts.

Without

capable manufacturing, all previous

r e l i abi l i ty

efforts

w i l l

provide

l i t t le

or no benefit.

- 7 -


19/28

ACCELERATED TESTING

180-

160-

140-

o

120-

3

100-

8 0

6 0

4 0

2 0

u

Upper Specification

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100105110

Late ra lRunout (Sys tem)

igur

1.4

Tolerance

stackup at a 3-sigma quality

level

300

250-

Upper Specification

u

c

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