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    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.

    -247-

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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-

    http://www.itl.nist.gov/div898/http://www.itl.nist.gov/div898/
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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

    -249-

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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

    -250-

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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

    - 2 5 1 -

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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

    -252-

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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

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    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

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    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.