Basic Descriptive Statistics Populations and Samples Histograms and Frequency Functions Cumulative Frequency Function The Cumulative Distribution Function and the Probability Density Function Probability Concepts Random Variables Sample Estimates of Population Parameters How to Use Descriptive Statistics Data Simulation Reliability Concepts Reliability Function Some Important Probabilities Hazard Function or Failure Rate Cumulative Hazard Function Average Failure Rate Units Bathtub Curve for Failure Rates Recurrence and Renewal Rates Mean Time to Failure and Residual Lifetime Types of Data Failure Mode Separation Exponential Distribution Exponential Distribution Basics The Mean Time to Fail for the Exponential The Exponential Lack of Memory Property Areas of Application for the Exponential Exponential Models with Duty Cycles and Failure on Demand Estimation of the Exponential Failure Rate λ Exponential Distribution Closure Property Testing Goodness of Fit--the Chi-Square Test Testing Goodness of Fit--Empirical Distribution Function Tests Confidence Bounds for λ and the MTTF The Case of Zero Failures Planning Experiments Using the Exponential Distribution Simulating Exponential Random Variables The Two-Parameter Exponential Distribution Test Planning Via Spreadsheet Functions Determining the Sample Size EDF Goodness-of-Fits Tests Using Spreadsheets KS Test Weibull Distribution Empirical Derivation of the Weibull Distribution Properties of the Weibull Distribution Extreme Value Distribution Relationship. Areas of Application Weibull Parameter Estimation: Maximum Likelihood Estimation Method Weibull Parameter Estimation: Linear Rectification Simulating Weibull Random Variables The Three-Parameter Weibull Distribution Goodness of Fit for the Weibull Using a Spreadsheet to Obtain Weibull MLES Using a Spreadsheet to Obtain Weibull MLES for Truncated Data Spreadsheet Likelihood Profile Confidence Intervals for Weibull Parameters The Normal and Lognormal Distributions Normal Distribution Basics Applications of the Normal Distribution The Central Limit Theorem Normal Distribution Parameter Estimation Simulating Normal Random Variables The Lognormal Life Distribution Properties of the Lognormal Distribution Lognormal Distribution Areas of Application Lognormal Parameter Estimation Some Useful Lognormal Equations Simulating Lognormal Random Variables Using a Spreadsheet to Obtain Lognormal MLEs Using a Spreadsheet to Obtain Lognormal MLEs for Interval Data Reliability Data Plotting Properties of Straight Lines Least Squares Fit (Regression Analysis) Rectification Probability Plotting for the Exponential Distribution Probability Plotting for the Weibull Distribution Probability Plotting for the Normal and Lognormal Distributions Simultaneous Confidence Bands Order Statistics and Median Ranks Analysis of Multicensored Data Multicensored Data Analysis of Interval (Readout) Data Life Table Data Left-Truncated and Right-Censored Data Left-Censored Data Other Sampling Schemes (Arbitrary Censoring: Double and Overlapping Interval Censoring)--Peto-Turnbull Estimator Simultaneous Confidence Bands for the Failure Distribution (or Survival) Function Cumulative Hazard Estimation for Exact Failure Times Johnson Estimator Obtaining Bootstrap Confidence Bands Using a Spreadsheet Physical Acceleration Models Accelerated Testing Theory Exponential Distribution Acceleration Acceleration Factors for the Weibull Distribution Likelihood Ratio Tests of Models Confidence Intervals Using the LR Method Lognormal Distribution Acceleration Acceleration Models The Arrhenius Model Estimating ΔH with More Than Two Temperatures Eyring Model Other Acceleration Models Acceleration and Burn-In Life Test Experimental Design An Alternative JMP Input for Weibull Analysis of High-Stress Failure Data Using a Spreadsheet for Weibull Analysis of High-Stress Failure Data Using A Spreadsheet for MLE Confidence Bounds for Weibull Shape Parameter Using a Spreadsheet for Lognormal Analysis of the High-Stress Failure Data Shown in Table 8.5 Using a Spreadsheet for MLE Confidence Bounds for the Lognormal Shape Parameter Using a Spreadsheet for Arrhenius-Weibull Model Using a Spreadsheet for MLEs for Arrhenius-Power Relationship Lognormal Model Spreadsheet Templates for Weibull or Lognormal MLE Analysis Alternative Reliability Models Step Stress Experiments Degradation Models Lifetime Regression Models The Proportional Hazards Model Defect Subpopulation Models Summary JMP Solution for Step Stress Data in Example 9.1 Lifetime Regression Solution Using Excel JMP Likelihood Formula for the Defect Model JMP Likelihood Formulas for Multistress Defect Model Example System Failure Modeling: Bottom-Up Approach Series System Models The Competing Risk Model (Independent Case) Parallel or Redundant System Models Standby Models and the Gamma Distribution Complex Systems System Modeling: Minimal Paths and Minimal Cuts General Reliability Algorithms Burn-In Models The "Black Box" Approach--An Alternative to Bottom-Up Methods Quality Control in Reliability: Applications of Discrete Distributions Sampling Plan Distributions Nonparametric Estimates Used with the Binomial Distribution Confidence Limits for the Binomial Distribution Normal Approximation for Binomial Distribution Confidence Intervals Based on Binomial Hypothesis Tests Simulating Binomial Random Variables Geometric Distribution Negative Binomial Distribution Hypergeometric Distribution and Fisher''s Exact Test Poisson Distribution Types of Sampling Generating a Sampling Plan Minimum Sample Size Plans Nearly Minimum Sampling Plans Relating an OC Curve to Lot Failure Rates Statistical Process Control Charting for Reliability Repairable Systems Part I: Nonparametric Analysis and Renewal Processes Repairable versus Nonrepairable Systems Graphical Analysis of a Renewal Process Analysis of a Sample of Repairable Systems Confidence Limits for the Mean Cumulative Function (Exact Age Data) Nonparametric Comparison of Two MCF Curves Renewal Processes. Homogeneous Poisson Process MTBF and MTTF for a Renewal Process MTTF and MTBF Two-Sample Comparisons Availability Renewal Rates Simulation of Renewal Processes Superposition of Renewal Processes CDF Estimation from Renewal Data (Unidentified Replacement) True Confidence Limits for the MCF Cox F-Test for Comparing Two Exponential Means Alternative Approach for Estimating CDF Using the Fundamental Renewal Equation Repairable Systems Part II: Nonrenewal Processes Graphical Analysis of Nonrenewal Processes Two Models for a Nonrenewal Process Testing for Trends and Randomness Laplace Test for Trend Reverse Arrangement Test Combining Data from Several Tests Nonhomogeneous Poisson Processes Models for the Intensity Function of an NHPP Rate of Occurrence of Failures Reliability Growth Models Simulation of Stochastic Processes Bayesian Reliability Evaluation Classical versus Bayesian Analysis Classical versus Bayes System Reliability Bayesian System MTBF Evaluations Bayesian Estimation of the Binomial p The Normal/Normal Conjugate Prior Informative and Noninformative Priors A Survey of More Advanced Bayesian Methods Gamma and Chi-Square Distribution Relationships Problems Answers to Selected Exercises References Index n Basics The Mean Time to Fail for the Exponential The Exponential Lack of Memory Property Areas of Application for the Exponential Exponential Models with Duty Cycles and Failure on Demand Estimation of the Exponential Failure Rate λ Exponential Distribution Closure Property Testing Goodness of Fit--the Chi-Square Test Testing Goodness of Fit--Empirical Distribution Function Tests Confidence Bounds for λ and the MTTF The Case of Zero Failures Planning Experiments Using the Exponential Distribution Simulating Exponential Random Variables The Two-Parameter Exponential Distribution Test Planning Via Spreadsheet Functions Determining the Sample Size EDF Goodness-of-Fits Tests Using Spreadsheets KS Test Weibull Distribution Empirical Derivation of the Weibull Distribution Properties of the Weibull Distribution Extreme Value Distribution Relationship. Areas of Application Weibull Parameter Estimation: Maximum Likelihood Estimation Method Weibull Parameter Estimation: Linear Rectification Simulating Weibull Random Variables The Three-Parameter Weibull Distribution Goodness of Fit for the Weibull Using a Spreadsheet to Obtain Weibull MLES Using a Spreadsheet to Obtain Weibull MLES for Truncated Data Spreadsheet Likelihood Profile Confidence In.