Reliability Modelling: A Statistical Approach

TLDR: BASIC CONCEPTS Introduction Events and Probability Rules of Probability Dependent Events Random Variables and probabilities Distributions The Reliability Function The Hazard Function Expectation COMMON LIFETIME MODELS Introduction Graphical Methods Testing for Trend Repair Time Maintainability and Availability Introduction to Renewal Theory Laplace Transforms The Renewal Function Alternating Renewal Processes The Distribution of N(t) system RELIABILITY Systems and System Logic Tie and Cut Sets Probability Bounds Fault Trees Failure Over Time Redundancy Quorum or m-out-of

Abstract: BASIC CONCEPTS Introduction Events and Probability Rules of Probability Dependent Events Random Variables and Probability Distributions The Reliability Function The Hazard Function Expectation COMMON LIFETIME MODELS Introduction The Poisson Process The Weibull Distribution The Gumbel Distribution The Normal and Lognormal Distributions The Gamma Distribution The Logistic and Log Logistic Distributions The Pareto Distribution Order Statistic and Extreme Value Distributions MODEL SELECTION Introduction Non-Parametric Estimation of R(t) and h(t) Censoring Kaplan-Meier Estimator Graphical Methods Straight Line Fitting Weibull Plotting Normal Plotting Other Model Family Plots Comparison of Distributions MODEL FITTING Parameter Estimation The Variance of Estimators Confidence Interval Estimates Maximum Likelihood Estimating Quantities Estimation Methods Using Sample Moments General Probability Plots Goodness of Fit Pearson's Chi-squared Test Kolmogorov-Smirnov Test Tests for Normality A-squared and W-squared Tests Stabilized Probability Plots Censored Data REPAIRABLE SYSTEMS Introduction Graphical Methods Testing for Trend Repair Time Maintainability and Availability Introduction to Renewal Theory Laplace Transforms The Renewal Function Alternating Renewal Processes The Distribution of N(t) SYSTEM RELIABILITY Systems and System Logic Tie and Cut Sets Probability Bounds Fault Trees Failure Over Time Redundancy Quorum or m-out-of-n Systems Analysis of Systems Using State Spaces Mean Time to Fail (MTTF) Considerations Due to "Switching" Common Cause Failures MODELS FOR FUNCTIONS OF RANDOM VARIABLES Combinations and Transformations of Random Variables Expectations of Functions of Random Variables Approximations for E[g(x)] and V[g(x)] Distribution of a Function of Random Variables Probabilistic Engineering Design Stress and Strength Distributions Interference Theory and Reliability Computations Normally Distributed Stress and Strength Safety Factors and Reliability Graphical Approach for Empirically Determined Distributions MAINTENANCE STRATEGIES Maintained Systems Availability Markovian Systems Mean Time between Failures (MTBF) Age Replacement Scheduled Maintenance Systems with Failure Detection/Fail Safe Devices Down-Time Distributions LIFE TESTING AND INFERENCE Life Test Plans Prediction of Time on Test Inference for the Exponential Distribution The Effect of Data Rounding Parametric Reliability Bounds Likelihood-Based Methods The Likelihood Ratio Test Binomial Experiments Non-Parametric Estimation and Confidence Intervals for R(t) Estimating System Reliability from Subsystem Test Data Accelerated Testing ADVANCED MODELS Covariates Proportional Hazards Models Accelerated Life Models Mixture Models Competing Risks Dependent Failures Load-Sharing Systems Bayesian Reliability Case Studies USEFUL MATHEMATICAL TECHNIQUES Partial Fractions Series Taylor Expansions Newton-Raphson Iteration Numerical Integration Matrix Algebra The Principle of Least Squares