Applied Reliability

Since the publication of the second edition of Applied Reliability in 1995, the ready availability of inexpensive, powerful statistical software has changed the way statisticians and engineers look at and analyze all kinds of data. Problems in reliability that were once difficult and time consuming even for experts can now be solved with a few well-chosen clicks of a mouse. However, software documentation has had difficulty keeping up with the enhanced functionality added to new releases, especially in specialized areas such as reliability analysis.

Using analysis capabilities in spreadsheet software and two well-maintained, supported, and frequently updated, popular software packages—Minitab and SAS JMP—the third edition of Applied Reliabilityis an easy-to-use guide to basic descriptive statistics, reliability concepts, and the properties of lifetime distributions such as the exponential, Weibull, and lognormal. The material covers reliability data plotting, acceleration models, life test data analysis, systems models, and much more. The third edition includes a new chapter on Bayesian reliability analysis and expanded, updated coverage of repairable system modeling.

Taking a practical and example-oriented approach to reliability analysis, this book provides detailed illustrations of software implementation throughout and more than 150 worked-out examples done with JMP, Minitab, and several spreadsheet programs. In addition, there are nearly 300 figures, hundreds of exercises, and additional problems at the end of each chapter, and new material throughout. Software and other files are available for download online

Dr. David C. Trindade is the chief officer of best practices and fellow at Bloom Energy. He was previously a distinguished principal engineer at Sun Microsystems, senior director of software quality at Phoenix Technologies, senior fellow and director of reliability and applied statistics at Advanced Micro Devices, worldwide director of quality and reliability at General Instruments, and advisory engineer at IBM. He has also been an adjunct lecturer at the University of Vermont and Santa Clara University, teaching courses in statistical analysis, reliability, probability, and applied statistics. In 2008, he was the recipient of the IEEE Reliability Society’s Lifetime Achievement Award.

Basic Descriptive StatisticsPopulations and SamplesHistograms and Frequency FunctionsCumulative Frequency FunctionThe Cumulative Distribution Function and the Probability Density FunctionProbability ConceptsRandom VariablesSample Estimates of Population ParametersHow to Use Descriptive StatisticsData SimulationReliability ConceptsReliability FunctionSome Important ProbabilitiesHazard Function or Failure RateCumulative Hazard FunctionAverage Failure RateUnitsBathtub Curve for Failure RatesRecurrence and Renewal RatesMean Time to Failure and Residual LifetimeTypes of DataFailure Mode SeparationExponential DistributionExponential Distribution BasicsThe Mean Time to Fail for the ExponentialThe Exponential Lack of Memory PropertyAreas of Application for the ExponentialExponential Models with Duty Cycles and Failure on DemandEstimation of the Exponential Failure Rate λ Exponential Distribution Closure PropertyTesting Goodness of Fit—the Chi-Square TestTesting Goodness of Fit—Empirical Distribution Function TestsConfidence Bounds for λ and the MTTFThe Case of Zero FailuresPlanning Experiments Using the Exponential DistributionSimulating Exponential Random VariablesThe Two-Parameter Exponential DistributionTest Planning Via Spreadsheet FunctionsDetermining the Sample SizeEDF Goodness-of-Fits Tests Using SpreadsheetsKS TestWeibull DistributionEmpirical Derivation of the Weibull DistributionProperties of the Weibull DistributionExtreme Value Distribution Relationship.Areas of ApplicationWeibull Parameter Estimation: Maximum Likelihood Estimation MethodWeibull Parameter Estimation: Linear RectificationSimulating Weibull Random VariablesThe Three-Parameter Weibull DistributionGoodness of Fit for the WeibullUsing a Spreadsheet to Obtain Weibull MLESUsing a Spreadsheet to Obtain Weibull MLES for Truncated DataSpreadsheet Likelihood Profile Confidence Intervals forWeibull ParametersThe Normal and Lognormal DistributionsNormal Distribution BasicsApplications of the Normal DistributionThe Central Limit TheoremNormal Distribution Parameter EstimationSimulating Normal Random VariablesThe Lognormal Life DistributionProperties of the Lognormal DistributionLognormal Distribution Areas of ApplicationLognormal Parameter EstimationSome Useful Lognormal EquationsSimulating Lognormal Random VariablesUsing a Spreadsheet to Obtain Lognormal MLEsUsing a Spreadsheet to Obtain Lognormal MLEs for Interval DataReliability Data PlottingProperties of Straight LinesLeast Squares Fit (Regression Analysis)RectificationProbability Plotting for the Exponential DistributionProbability Plotting for the Weibull DistributionProbability Plotting for the Normal and Lognormal DistributionsSimultaneous Confidence BandsOrder Statistics and Median RanksAnalysis of Multicensored DataMulticensored DataAnalysis of Interval (Readout) DataLife Table DataLeft-Truncated and Right-Censored DataLeft-Censored DataOther Sampling Schemes (Arbitrary Censoring: Double and Overlapping Interval Censoring)—Peto–Turnbull EstimatorSimultaneous Confidence Bands for the FailureDistribution (or Survival) FunctionCumulative Hazard Estimation for Exact Failure TimesJohnson EstimatorObtaining Bootstrap Confidence Bands Using a SpreadsheetPhysical Acceleration ModelsAccelerated Testing TheoryExponential Distribution AccelerationAcceleration Factors for the Weibull DistributionLikelihood Ratio Tests of ModelsConfidence Intervals Using the LR MethodLognormal Distribution AccelerationAcceleration ModelsThe Arrhenius ModelEstimating ΔH with More Than Two TemperaturesEyring ModelOther Acceleration ModelsAcceleration and Burn-InLife Test Experimental DesignAn Alternative JMP Input for Weibull Analysis of High-Stress Failure DataUsing a Spreadsheet for Weibull Analysis of High-Stress Failure DataUsing A Spreadsheet for MLE Confidence Bounds for Weibull Shape ParameterUsing a Spreadsheet for Lognormal Analysis of the High-Stress Failure Data Shown in Table 8.5Using a Spreadsheet for MLE Confidence Bounds for the Lognormal Shape ParameterUsing a Spreadsheet for Arrhenius–Weibull ModelUsing a Spreadsheet for MLEs for Arrhenius–Power Relationship Lognormal ModelSpreadsheet Templates for Weibull or Lognormal MLE AnalysisAlternative Reliability ModelsStep Stress ExperimentsDegradation ModelsLifetime Regression ModelsThe Proportional Hazards ModelDefect Subpopulation ModelsSummaryJMP Solution for Step Stress Data in Example 9.1Lifetime Regression Solution Using ExcelJMP Likelihood Formula for the Defect ModelJMP Likelihood Formulas for Multistress Defect Model ExampleSystem Failure Modeling: Bottom-Up ApproachSeries System ModelsThe Competing Risk Model (Independent Case)Parallel or Redundant System ModelsStandby Models and the Gamma DistributionComplex SystemsSystem Modeling: Minimal Paths and Minimal CutsGeneral Reliability AlgorithmsBurn-In ModelsThe "Black Box" Approach—An Alternative to Bottom-Up MethodsQuality Control in Reliability: Applications of Discrete DistributionsSampling Plan DistributionsNonparametric Estimates Used with the Binomial DistributionConfidence Limits for the Binomial DistributionNormal Approximation for Binomial DistributionConfidence Intervals Based on Binomial Hypothesis TestsSimulating Binomial Random VariablesGeometric DistributionNegative Binomial DistributionHypergeometric Distribution and Fisher’s Exact TestPoisson DistributionTypes of SamplingGenerating a Sampling PlanMinimum Sample Size PlansNearly Minimum Sampling PlansRelating an OC Curve to Lot Failure RatesStatistical Process Control Charting for ReliabilityRepairable Systems Part I: Nonparametric Analysis and Renewal ProcessesRepairable versus Nonrepairable SystemsGraphical Analysis of a Renewal ProcessAnalysis of a Sample of Repairable SystemsConfidence Limits for the Mean Cumulative Function (Exact Age Data)Nonparametric Comparison of Two MCF CurvesRenewal Processes.Homogeneous Poisson ProcessMTBF and MTTF for a Renewal ProcessMTTF and MTBF Two-Sample ComparisonsAvailabilityRenewal RatesSimulation of Renewal ProcessesSuperposition of Renewal ProcessesCDF Estimation from Renewal Data (Unidentified Replacement) True Confidence Limits for the MCFCox F-Test for Comparing Two Exponential MeansAlternative Approach for Estimating CDF Using theFundamental Renewal EquationRepairable Systems Part II: Nonrenewal ProcessesGraphical Analysis of Nonrenewal ProcessesTwo Models for a Nonrenewal ProcessTesting for Trends and RandomnessLaplace Test for TrendReverse Arrangement TestCombining Data from Several TestsNonhomogeneous Poisson ProcessesModels for the Intensity Function of an NHPPRate of Occurrence of FailuresReliability Growth ModelsSimulation of Stochastic ProcessesBayesian Reliability EvaluationClassical versus Bayesian AnalysisClassical versus Bayes System ReliabilityBayesian System MTBF EvaluationsBayesian Estimation of the Binomial pThe Normal/Normal Conjugate PriorInformative and Noninformative PriorsA Survey of More Advanced Bayesian MethodsGamma and Chi-Square Distribution RelationshipsProblemsAnswers to Selected ExercisesReferencesIndex