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1/10
R E F E R E N C E S
Accelerated Testing Research: Special Publications
(2000), Societyof AutomotiveEngineers,
Warrendale,PA.
Chan,
H . Anthony (2001).
Accelerated Stress Testing Handbook: Guide for Achieving
Quality Products,
IEEE
Press,
Institute of Electrical and
Electronics
Engineers,
Piscataway,
NJ.
Dh i l l o n , B.S. (1985).
Quality Control, Reliability, and Engineering Design,
Marcel Dekker,
New York.
Dodson,
B.L. , and M.D. Mulcahy (1992).
Certified Reliability Engineer Examination
Study
Guide,
Quality Publishing,
Tucson,
AZ.
Dodson, Bryan (1994). Weibull Analysis with Software), ASQC Qua lity
Press,
Milwaukee, WI .
Dovich, R.A. (1990).
Reliability Statistics,
ASQC Quality
Press,
Milwaukee, WI .
Environmental Stress Screening Handbook
(2004), Thermotron Ltd. , Holland,
M I .
Fundamentals
of
Accelerated Stress Testing
(2004), Thermotron Ltd. , Holland, M I .
Hobbs, Gregg
K. (2000).
Accelerated Reliability Engineering: HALT and HASS,
JohnWiley
Sons,New York.
Ireson,
G.W., and C.F.Coombs(1996).
Handbook of Reliability Engineering and Management,
M cG r aw -H i l l,
New York.
Kapur, K.C., and L.R.Lamberson (1977).
Reliability in Engineering Design,
John Wiley &
Sons,New York.
Kie lp in sk i ,
T.J., and W. Nelson (1975). Optimum
CensoredAccelerated
L i f e
Tests
for Normal
and Lognormal L i f e Distributions, IEEE
Transactions on Reliability,
R-24:310-320,
Institute of Electrical and
Electronics
Engineers,
Piscataway,
NJ.
Krishnamoorthi, K.S. (1992).
Reliability Methods for Engineers,
ASQ Quality
Press,
Milwaukee, WI .
La l l ,
Pradeep,
Michael G.
Pecht,
and Edward B. Hakim, (1997). Influence of Temperature on
Microelectronics, CRC
Press,
Boca Raton,FL.
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ACCELERATED
TESTING
Lewis, E.E. (1995).
Introduction to Reliability Engineering,
JohnWiley &Sons,New York.
Meeker,
W., and W. Nelson (1976). Optimum
Accelerated
Li f eTestsfor Weibull and
Extreme
Value Distributions, IEEE Transactions on Reliability,
R-25:20-24,
Institute of Electri
cal and
ElectronicsEngineers, Piscataway,
NJ.
Meeker,W.Q., and G.J. Hahn (1985). How to Plan an Accelerated Life TestSome Practical
Guidelines,
ASQ QualityPress,Milwaukee, WI .
Nelson, W. (1990). Accelerated Testing: Statistical Models, Test Plans and Data Analysis,
JohnWiley &Sons,New York.
NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/
handbook/.
O'Connor, Patrick D.T. (2002). Practical Reliability Engineering,
John
Wiley &
Sons,
New York.
Shooman,M . L . (1990). Probabilistic Reliability: An Engineering Approach, RobertE. Krieger,
Malabar,FL.
Staudte,
Robert
G., and S.J. Sheather (1990). Robust Estimation and Testing, JohnWiley &
Sons,New York.
Tobias, PA., and D.C. Trindade (1995).
Applied Reliability,
Van Nostrand Reinhold, New
York .
U.S. Army MaterielSystemsAnalysis Ac t i v i t y (1999). Reliability Growth Handbook.
U.S.Departmentof
Defense.
M I L - HD BK - 18 9 : Reliability Growth Management, Naval Pub
lications and Forms
Center,
Philadelphia.
U.S.
Department
ofDefense. M I L - H D BK - 7 81 : Reliability Test Methods, Plans and Environ-
mentsfor Engineering Development, Qualification and Production, Naval
Publications
and FormsCenter, Philadelphia.
U.S. Department of
Defense.
MIL-STD-810: Environmental Test Methods and Engineering
Guidelines, Naval Publicationsand Forms
Center,
Philadelphia.
U.S.DepartmentofDefense. MIL-STD-1635: Reliability Growth Testing, Naval
Publications
and FormsCenter, Philadelphia.
Walker, N. Edward (1998).
The Design Analysis Handbook,
Newnes, Boston.
Young, W.R. (1998).
Accelerated
Temperature Pharmaceutical ProductStability Determina
tions, Drug Development and Industrial Pharmacy.
-248-
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I N D E X
Accelerated testing
ambiguities in , 17
models for, 141-180
plans for, 103-140
purposeof, 1-2
tolerances
in, 5-8
see
alsoTesting
Acceleration, linear, 141-142
Acceptance testing, 119-121, 208
Acronyms,
list
of, 243-245
Ai r f l ow , 189-190, 194-195,202
Altitude,
219
A M S A A (ArmyMaterial
SystemsAnalysis
Act iv i ty ) reliabil i tygrowthmodel, 139-140
Analogic Corporation,ESS program results,
197
Arrheniusmodel, 149-157
Automobileresale
value, 16
Bathtub
curve, 182
Bayes' theorem, 68-71
Bayesian testing, 110-118
determiningparameters
for, 113-115
Weibulldistribution in ,
110-115
Bendix
Corporation, ESS program results, 197
Bias,lack of, 73
Binomial
distribution,5658
Bogey testing, 99, 109
Burn-in
testing, 185, 191
optimizing, 202-204
Casehistories, 197-198
Censoreddata,20, 53
Center of
gravity,
29
Central
limit
theorem, 40
Chamber, 201,213
Changecontrol,12
Characteristic
life,
34
Chemical
reactions, 149
Chi-squaredistribution,62-64
Chi-square significance, 224-225r
Coffin-Masonmodel, 170-171
Combinedenvironmental screening, 192-193
Combinedenvironmental testing, 218
Computercontrol,202
Concept
validation,
10-11
Condensation, 213
Confidence intervals
nonparametric, 99, 101
for
normaldistribution, 86-87
for Weibulldistribution,93-94
Confidence
limits,
53
Consistency, 73
Continuous modelingdistributions,33-54
Continuous variables, 20-21
Corrosion,219
Cumulativedensityfunction
hypergeometric, 58
standardnormal,45
Cumulativedistribution function, 25-27
binomial,57
exponential,80
F- 67
lognormal,
47
normal,89
Poisson, 55,229f
inprobability
plotting,
74, 80
standard
normal,
222-223f
Weibul l ,
37, 97
Cumulativehazardfunction, 74
exponential, 79
normal,in hazard
plotting,
87
Weibul l ,
95
Customer requirements, understanding, 9-10
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ACCELERATED TESTING
Cyclic
testing, 215-216
Defect
exposure
tests,
208
Defect
rate, manufacturing, 6
Degradation
testing models, 171-177
Degrees
of freedom, 164
Designlife, determining,
2-5
Designvalidation,
11
Developmenttests,
1
Discrete modeling
distributions,
55-61
identifying correct
distribution,
61,62/
Discrete variables, 21
Distributions
binomial,
56-58
chi-square, 62-64
continuous
modeling,
33-54
discrete
modeling,
55-61
identifying correct
distribution,
6162/
exponential,50-54
parameter estimation for, 74-75
reliabili tyfunction wi th acceleration
factor,142r
in
sequential testing, 125-126
F-distribution,
66-68
geometric, 60-61
hypergeometric, 58-60
lognormal,46-50
parameter estimation for, 91
reliabili tyfunction with acceleration
factor,142r
normal,
39-46
hazardplottingfor, 87-89
maximumlikelihoodestimation for,
84-87
parameter estimation for, 83-91
probabilityplottingfor, 89-91
reliabili tyfunction wi th acceleration
factor,142/
Poisson, 55-56
posterior, 68
prior,
68
sampling,61-68
shapesof, comparing, 142-144
summary of, 71
f-distribution,
64-66
Weibull,
33-39
Bayesian, in sequential testing, 126-131
in
Bayesian testing, 110-115
hazardplottingfor, 95-96
maximum likelihoodestimation for,
92-94
parameter estimation for 92-99
probabilityplottingfor, 97-99
reliabili ty function wi th acceleration
factor, 142?
Duane reliabili tygrowthmodel, 136-138
Dust,219
Dynamic
screens,
195-196
Electrical
stress, 191,
218
Electrodynamic
shakers,
216, 217
Electronic
equipment, 184-185
estimatingshapeparameter for, 112-113
HALT
for, 179
reliabili tystandards
for, 149
Elephant
tests,
179
EngineeringDepartment, exampleresponse
from, 12
Environment,
test,207-208
Environmentalstress,
types of, 187-193
Environmental
stressscreening (ESS),
181-205
casehistories, 197-198
definitionof, 184
determining
screeninglevel, 199-200
equipment for, 200-202
evolutionof, 184-186
failureversus
productionlevel,200/
implementing
a program, 198-200
misconceptions about, 186-187
monitoring,
200
screencomplexitylevels, 195-196
screentypes, 193/
summary of, 205
Equipment
for
environmentalstress
screening, 200-202
test
methods and applications, 207-219
Estimation,
of parameters, 73-102
Exercised
screens,
196
Expectation, 29-30
Expected number oftrials, 124-125
Explosive
atmosphere, 219
Exponential
distribution,
50-54
parameter estimation for, 74-75
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INDEX
Exponentialdistribution
cont.)
reliabil i ty function withacceleration factor,
142?
in
sequential testing, 125-126
Eyring
model, 157-168
F-distribution,66-68
F
significance, 226-227?
Failure analysis, 196
Failure
costs,
13
Failure
modes, detection of, 135
Failure
modesand effects analysis ( FM EA ) ,10
Failure
rate, 203
Failure
rateanalysis and corrective actions sys
tem(FRACAS),10
Failure-truncated testing, 113-114
Feedback
loop,
for
reliabil i tygrowth,
135-136
Fieldcorrelation, 142-148
Field
reliabil i ty,
example performance, 14?
Finaldemonstration, 135
Finance Department, exampleresponse from,
12
Financialconsiderations, 9-17
Fixturing,202
Frequency domain, 214-215
Ful l
functional
screens,196
Fungus, 219
Gamma
function, 31 n,
62, 221?
Geometricdistribution,60-61
Glossary, 233-242
Hardfailures, 195
Hazardfunction, 27-29
exponential, 51-52
for
linear acceleration, 141
lognormal,
49-50
normal,45, 46/
Weibul l ,36
Hazardplotting,74, 79, 80/
for
normal
distribution,
87-89
for Weibulldistribution,
95-96
Hewlett-Packard, ESS program results,
197-198
Hiddenreliabil i tycosts,15
High-temperatureburn-in,191
Highlyaccelerated life testing (HALT) ,
179-180
Highly
accelerated
stress
screen
(HASS),
179-180
Histogram,example, 21 /
Hydraulictesting, 216-217
Hypergeometricdistribution, 58-60
Ic ing,
219
Infancyfailure, 182, 185
Infant
mortalityperiod, 36
Instantaneous
failure
rate, 27
InstituteofEnvironmentalSciences,186
Instrumentation, 202
Intelligentdesign, 10
Interconnects, 202
Keypersonnel, 198-199
Kurtosis,30
Latent defects, 182
Life
cycle patterns, 182
Likelihoodfunction,
74
Likelihoodratio,119
Linearacceleration, 141-142
Lineardegradation, 172
Load
cycles, randomization of, 131-134
Local information matrix,74
Locationparameter, 34,49
Lognormal
distribution,
46-50
parameter estimation for, 91
reliabil i ty function withacceleration factor,
142?
Loose cargo testing, 215
Low-temperature
screen,
192
Manufacturing, 11-12
Manufacturingdefect rate, 6-7
ManufacturingDepartment, example
response
from,
12
Material
handling,
202
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ACCELERATED
TESTING
Maximum likelihoodestimation, 73-79
for
normal
distribution,
84-87
for Weibull
distribution,
92-94
Mean,
29
of
binomial distribution,
57
of
exponential
distribution,
53
of geometric
distribution,
60
of
hypergeometricfunction, 58
of lognormal
distribution,
49
ofnormal distribution,83
of/-distribution,
64
ofWeibulldistribution,37, 38/
Mean
time tofail ,39, 103, 104/
Mechanical
crack
growth
model, 170-171
Mechanicalshock, 217-218
Mechanical
tools, 215
M i l it a r y
standards,
185
Mission profiletesting, 185
Models
accelerated testing, 141-180
A M S A A reliabili tygrowth,
139-140
Arrhenius, 149-157
Coffin-Mason, 170-171
degradation testing, 171-177
Duane reliabili tygrowth, 136-138
elephant
test,
179
Eyring, 157-168
field correlation, 142-148
HALT
andHASS, 179-180
linearacceleration, 141-142
mechanical crack
growth,
170-171
qualitative
test,
176-180
reliabili tygrowth,
136-140
step-stress
testing, 177-178
voltage,
169-170
M odif iedorder of
failure,
81
Moisture,
wind ,
andrain,219
Monitoredscreens,196
M ul ti p lecensoring, 20
Nonparametric confidence intervals, 99, 101
Normal distribution,
39-46
hazardplottingfor, 87-89
maximumlikelihoodestimation for, 84-87
parameterestimation for, 83-91
probability
plotting
for, 89-91
reliabili ty
function
with
acceleration factor,
142/
Objective,
environmental
stress
screening, 198
Operatingcharacteristic (OC) curve, 122-124
Parameterestimation, 73-102
Pass-fail testing, 119-124
Pneumatic actuators, 215-216
Poisson cumulative
distribution
function,229/
Poisson
distribution,
55-56
Posterior
distribution,
68
Powercycling,191
Power spectral density, 215
Power supplies, 202
Prior distribution,68
Probability,fundamentals of, 19-31
Probability
densityfunction, 21-25
binomial,
56-57
chi-square, 63
exponential,50-51,75
F - 66, 67/
geometric, 60
hypergeometric, 58
forlinear acceleration, 141
lognormal,
47, 91
normal,83
Poisson, 55
posterior, 68
prior,
68
standardnormal,40, 41 /
/- 64, 65/
Weibul l ,
33, 92
Probabilityplotting,74,80-83
fornormal
distribution,
89-91
for Weibulldistribution,97-99
Product electronics, 202
Productfailure modes, 181
Product
reliabili ty
equation, 181-183
Profile,201
Qualificationtests,208
Qualitative
tests, 176-180
Quality
assurance
tests,
1
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INDEX
Random sampling, 19-21
Random
vibration,
190-191, 193, 194, 214
Randomizationof load cycles, 131-134
Reaction rate, 149
Real
wor ld
environment,
defining,
209-211
Reliabilityconfidence limits ,81
Reliabilitycosts, hidden, 15
Reliabilitydemonstration sample sizes, 2/
Reliability
function,
27
wi thacceleration factor, 142/
exponential,51
forlinear acceleration, 141
lognormal,47
Weibul l ,36
Reliability
growth,
134-140
models for, 136-140
processfor, 135-136
Reliabilityprogram
elements of, 9-17
examplescores,13/
financial
considerations for, 9-17
Reliabilitytesting, 103
Sample size
determining,
5
effect
of, 105-109
effect
on test duration, 115-118
reliabili tydemonstration, 2/
Sampling,
19-21
Sampling distributions,
61-68
Scale parameter, 34
Screens
dynamic,
195-196
exercised, 196
full
functional,
196
monitored,
196
static, 195
Second moment-generating
function,
29
Sequential testing, 119-131
BayesianWeibull
distribution in,
126-131
exponentialdistribution in , 125-126
Shape,of
distributions,
comparing, 142-144
Shape
parameter, 33
determining
value of, 118
effect of, 110-112
estimating, 112-113
Shipping
and
handling,
207, 209, 211
Shockresponsespectra, 217
Simulationtesting, 208-211
Sine
vibration
fixed frequency, 192
swept frequency, 192
Sinusoidal
input, 211-212, 214
Skewness, 30
Slip
table, 216
Soft
failures, 195
Standard
deviation,
of
normal
distribution,84
Standard normal cumulative density
function,
45
Standard normal cumulative
distribution
func
t ion,
47,222-223/
Standard normal
probability
density
function,
40,41/
Static
screens,
195
Statistical
sampling, 5
Steady
state
thermal testing, 212-213
Step-stress
testing, 177-178
Stimulationtesting, 211-212
Storage, 207, 209,210-211
Stress,
types of, 212-219
Stress
screening, environmental (ESS),
181-205
Stressuniformity,
194
Submersion, 219
Sufficiency,
73
Suppliers, in environmentalstressscreening,
198
Surfaced problems, 135
/Significance, 228
/-Distribution, 64-66
Temperature
cycling,
185, 187-190, 213
advantages
of, 193-195
Temperature testing, 212-214
Test
duration,
114-115
effect
of sample size on, 115-118
Testing
acceptance,
119-121, 208
Bayesian, 110-118
determining
parameters, 113-115
Weibull
distribution in ,
110-115
bogey, 99, 109
burn-in,
185, 191
optimizing,202-204
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ACCELERATED TESTING
Testing cont.)
combined environmental,
218
cyclic,
215-216
defect exposure, 208
development, 1
electricalstress,218
electrodynamic, 216, 217
equipment methods and applications,
207-219
failure-truncated,
113-114
hydraulic,
216-217
loose cargo, 215
mechanical, 215
mechanical shock, 217-218
mission
profile,
185
pass-fail,
119-124
pneumatic, 215-216
qualification,208
qualityassurance,
1
sequential, 119-131
BayesianWeibulldistributionin,
126-131
exponentialdistribution in ,
125-126
simulation,
208-211
stimulation, 211-212
temperature, 212-214
thermal,steady state,212-213
time-truncated,
114
vibration,
185, 190-191, 192, 214-218
zero-failure, 109-118
guidelines for, 115-118
see
also
Accelerated testing
Thermalexpansion, 212
Thermal
shock, 192, 213-214
Time
domain, 214-215
Time
history pulse, 217
Time-truncatedtesting, 114
Tolerances
determining, 5-8
number of
combinations,
6/
worst-case, 5-8
Transitiontemperature of metals, 212
Type
I error, 106-109
Type error, 106, 109
U.S.
government documents, 231-232
Ultraviolet,
219
Unforeseen deficiencies, 134-135
Uni t ,
uniform
random number generation,
131-134
Userprofiles, 2-4
Variance,
29
of
binomial distribution,57
ofestimates,
74
ofexponentialdistribution,51
ofgeometricdistribution,60
ofhypergeometricfunction, 58
of
lognormal distribution,
49
minimum,
73
of
/-distribution,64
ofWeibull
distribution,37, 38/, 93
Vibration
testing, 185, 190-191, 192, 214-218
Voltage
margining,
191
Voltagemodels, 169-170
Wearoutperiod,36
Weibull
distribution,33-39
Bayesian, in sequential testing, 126-131
inBayesian testing, 110-115
hazard
plotting
for, 95-96
maximumlikelihood
estimation for, 92-94
parameter
estimation for 92-99
probabilityplotting
for, 97-99
reliabil i ty
function
with
acceleration factor,
142/
Zero-failure
testing, 109-118
guidelines
for, 115-118
7/25/2019 12. Accelerated Testing - References & Index
9/10
B O U TT H E UT HOR S
ryanDodson
is the Director of
Reliability
Engineering
at Visteon in Dearborn,
Michigan.
He formerly was the
Manager of
Reliability
Engineering and
Quality
Informa
t i on
Systemsfor Continental Teves, Brake andChassis,
North
America. Prior to
joining
Continental Teves,
Dr.
Dodson held the positions of
Total
Quality Manage
ment
(T Q M )
Leader and
Reliability
Leader at
Alcoa
and
the position ofIndustrialEngineer at
Morton Th i oko l .
Dr.
Dodson has authored
seven
books and
five
com
mercial software programs, including the
Reliability
Engineering Handbook, Weibull
Analysis:
with Software,
and Certified
Reliability Engineer Examination Study
Guide. He
also
is the author of the International Quality
Federation's Six Sigma certification exam.
Dr.
Dodson holds a B.S. in petroleum engineering, an
M.S.
inindustrialengineering, an
M . B .A . ,
and a Doctor of
BusinessAdministration.
In addition,
he is a Certified Quality Engineer (CQE), a Certified
Reliability
Engineer (CRE), a Six Sigma
Master Black Belt, and a licensed Professional Engineer in Michigan and Indiana.
H a r r ySchwabhas almost
for tyyears
of experience as an
engineer, specializing in structural dynamics and vibra
tions. He holds a BachelorofAerospace Engineering
from
the Georgia Institute of
Technology,
an
M.S.
in Engineer
ing
Mechanics
f rom
the University of
MissouriRolla,
and an
M . B .A . f rom
the Florida Institute of Technology.
M r .
Schwab has worked
in
the
aerospace,
automotive, and
commercial
industries. The products
wi th
which he has
beeninvolved
include automobiles, trucks, railroad freight
cars,
aircraft,
boats,
and guided missiles. He has many
years
of experience inworking
wi th
random vibrations
and developed a method for deriving laboratory testing
-255-
7/25/2019 12. Accelerated Testing - References & Index
10/10
ACCELERATED TESTING
environments fromnon-stationary data. This technique can be used to accurately simulate real-
wo r l denvironments
while
greatly decreasing
test
time.
M r . Schwab has authored several technicalpapers for SAE International and the Institute of
Environmental
Sciences
and Technology
(IEST),
as
we l l
as for other technical organizations
and
publications.
Thesecover the fields ofvibrationtesting and analysis. He developed innova
tivetesting techniques for both the aerospaceand automotive industries, and he is a registered
Professional Engineer in
Missouri
and Florida.