Introduction to Reliability Analysis

1. System Effectiveness.- 1.1 Basic Concepts and Relationships.- 1.2 Time Categories.- 1.3 Reliability and Related Functions.- 1.4 Availability, Maintainability and Repairability.- 1.5 Exercises.- 2. Life Distributions, Models and Their Characteristics.- 2.1 Types of Failure Observations.- 2.2 General Characteristics of Life Distributions.- 2.3 Some Families of Life Distributions.- 2.3.1 Exponential and Shifted Exponential Distributions.- 2.3.2 Erlang, Chi-Square and Gamma Distributions.- 2.3.3 Weibull Distributions.- 2.3.4 Extreme Value Distributions.- 2.3.5 The Normal and Truncated Normal Distributions.- 2.3.6 Normal Approximations.- 2.3.7 Lognormal Distributions.- 2.3.8 Auxiliary Distributions: t and F.- 2.4 Discrete Distributions of Failure Counts.- 2.4.1 Distributions of Discrete Random Variables.- 2.4.2 The Binomial Distribution.- 2.4.3 The Poisson Distribution.- 2.4.4 Hypergeometric Distributions.- 2.5 Exercises.- 3. Reliability of Composite Systems.- 3.1 System Reliability for Series and Active Parallel Independent Components.- 3.2 k Out of n Systems of Independent Components.- 3.3 The Decomposition Method.- 3.4 Minimal Paths and Cuts.- 3.5 The MTTF of Composite Systems.- 3.6 Sequentially Operating Components.- 3.7 Fault Tree Analysis.- 3.8 Exercises.- 4. Reliability of Repairable Systems.- 4.1 The Renewal Process.- 4.2 The Renewal Function and Its Density.- 4.3 Asymptotic Approximations.- 4.4 Increasing the Availability by Preventive Maintenance and Standby Systems.- 4.4.1 Systems with Standby and Repair.- 4.4.2 Preventive Maintenance.- 4.5 Exercises.- 5. Graphical Analysis of Life Data.- 5.1 Probability Plotting for Parametric Models with Uncensored Data.- 5.2 Probability Plotting with Censored Data.- 5.3 Non-Parametric Plotting.- 5.3.1 Product Limit Estimator of Reliability.- 5.3.2 Total Time on Test Plots.- 5.4 Graphical Aids.- 5.5 Exercises.- 6. Estimation of Life Distributions and System Characteristics.- 6.1 Properties of Estimators.- 6.1.1 The Estimation Problem.- 6.1.2 Sampling Distributions, Accuracy and Precision.- 6.1.3 Closeness Probabilities.- 6.1.4 Confidence and Prediction Intervals.- 6.1.4.1 Estimating the Parameters of a Normal Distribution.- 6.1.4.2 Estimating the Reliability Function for an Exponential Distribution.- 6.2 Maximum Likelihood Estimation.- 6.2.1 Single-Parameter Distributions.- 6.2.1.1 Derivation.- 6.2:1.2 The Invariance Property.- 6.2.1.3 The Variance of an MLE.- 6.2.2 Multiparameter Distributions.- 6.3 MLE of System Reliability.- 6.4 MLE from Censored Samples—Exponential Life Distributions.- 6.4.1 Type I Censored Data.- 6.4.2 Type II Censored Data.- 6.5 The Kaplan-Meier PL Estimator as an MLE of R(t): Non-Parametric Approach.- 6.6 Exercises.- 7. Maximum Likelihood Estimators and Confidence Intervals for Specific Life Distributions.- 7.1 Exponential Distributions.- 7.2 Shifted Exponential Distributions.- 7.3 Erlang Distributions.- 7.4 Gamma Distributions.- 7.5 Weibull Distributions.- 7.6 Extreme Value Distributions.- 7.7 Normal and Lognormal Distributions.- 7.8 Truncated Normal Distributions.- 7.9 Exercises.- 8. Bayesian Reliability Estimation and Prediction.- 8.1 Prior and Posterior Distributions.- 8.2 Loss Functions and Bayes Estimators.- 8.2.1 Distribution-Free Bayes Estimator of Reliability.- 8.2.2 Bayes Estimator of Reliability for Exponential Life Distributions.- 8.3 Bayesian Credibility and Prediction Intervals.- 8.3.1 Distribution-Free Reliability Estimation.- 8.3.2 Exponential Reliability Estimation.- 8.3.3 Prediction Intervals.- 8.4 Credibility Intervals for the Asymptotic Availability of Repairable Systems: The Exponential Case.- 8.5 Empirical Bayes Method.- 8.6 Exercises.- 9. Reliability Demonstration: Testing and Acceptance Procedures.- 9.1 Reliability Demonstration.- 9.2 Binomial Testing.- 9.3 Exponential Distributions.- 9.4 Sequential Reliability Testing.- 9.4.1 The SPRT for Binomial Data.- 9.4.2 The SPRT for Exponential Lifetimes.- 9.5 Sequential Tests for Poisson Processes.- 9.6 Bayesian Reliability Demonstration Tests.- 9.7 Accelerated Life Testing.- 9.8 Exercises.- Annotated Bibliography.- Appendix of Statistical Tables.