Practical Applications of Bayesian Reliability.

Cover -- Title Page -- Copyright -- Contents -- Preface -- Acknowledgments -- About the Companion Website -- Chapter 1 Basic Concepts of Reliability Engineering -- 1.1 Introduction -- 1.1.1 Reliability Definition -- 1.1.2 Design for Reliability and Design for Six Sigma -- 1.2 Basic Theory and Concepts of Reliability Statistics -- 1.2.1 Random Variables -- 1.2.2 Discrete Probability Distributions -- 1.2.3 Continuous Probability Distributions -- 1.2.4 Properties of Discrete and Continuous Random Variables -- 1.2.4.1 Probability Mass Function -- 1.2.4.2 Probability Density Function -- 1.2.4.3 Cumulative Distribution Function -- 1.2.4.4 Reliability or Survival Function -- 1.2.4.5 Hazard Rate or Instantaneous Failure Rate -- 1.2.4.6 Cumulative Hazard Function -- 1.2.4.7 The Average Failure Rate Over Time -- 1.2.4.8 Mean Time to Failure -- 1.2.4.9 Mean Number of Failures -- 1.2.5 Censored Data -- 1.2.6 Parametric Models of Time to Failure Data -- 1.2.7 Nonparametric Estimation of Survival -- 1.2.8 Accelerated Life Testing -- 1.3 Bayesian Approach to Reliability Inferences -- 1.3.1 Brief History of Bayes' Theorem and Bayesian Statistics -- 1.3.2 How Does Bayesian Statistics Relate to Other Advances in the Industry? -- 1.3.2.1 Advancement of Predictive Analytics -- 1.3.2.2 Cost Reduction -- 1.4 Component Reliability Estimation -- 1.5 System Reliability Estimation -- 1.6 Design Capability Prediction (Monte Carlo Simulations) -- 1.7 Summary -- References -- Chapter 2 Basic Concepts of Bayesian Statistics and Models -- 2.1 Basic Idea of Bayesian Reasoning -- 2.2 Basic Probability Theory and Bayes' Theorem -- 2.3 Bayesian Inference (Point and Interval Estimation) -- 2.4 Selection of Prior Distributions -- 2.4.1 Conjugate Priors -- 2.4.2 Informative and Non‐informative Priors -- 2.5 Bayesian Inference vs. Frequentist Inference.

2.6 How Bayesian Inference Works with Monte Carlo Simulations -- 2.7 Bayes Factor and its Applications -- 2.8 Predictive Distribution -- 2.9 Summary -- References -- Chapter 3 Bayesian Computation -- 3.1 Introduction -- 3.2 Discretization -- 3.3 Markov Chain Monte Carlo Algorithms -- 3.3.1 Markov Chains -- 3.3.1.1 Monte Carlo Error -- 3.3.2 Metropolis-Hastings Algorithm -- 3.3.3 Gibbs Sampling -- 3.4 Using BUGS/JAGS -- 3.4.1 Define a JAGS Model -- 3.4.2 Create, Compile, and Run the JAGS Model -- 3.4.3 MCMC Diagnostics and Output Analysis -- 3.4.3.1 Summary Statistics -- 3.4.3.2 Trace Plots -- 3.4.3.3 Autocorrelation Plots -- 3.4.3.4 Cross‐Correlation -- 3.4.3.5 Gelman-Rubin Diagnostic and Plots -- 3.4.4 Sensitivity to the Prior Distributions -- 3.4.5 Model Comparison -- 3.5 Summary -- References -- Chapter 4 Reliability Distributions (Bayesian Perspective) -- 4.1 Introduction -- 4.2 Discrete Probability Models -- 4.2.1 Binomial Distribution -- 4.2.2 Poisson Distribution -- 4.3 Continuous Models -- 4.3.1 Exponential Distribution -- 4.3.2 Gamma Distribution -- 4.3.3 Weibull Distribution -- 4.3.3.1 Fit Data to a Weibull Distribution -- 4.3.3.2 Demonstrating Reliability using Right‐censored Data Only -- 4.3.4 Normal Distribution -- 4.3.5 Lognormal Distribution -- 4.4 Model and Convergence Diagnostics -- References -- Chapter 5 Reliability Demonstration Testing -- 5.1 Classical Zero‐failure Test Plans for Substantiation Testing -- 5.2 Classical Zero‐failure Test Plans for Reliability Testing -- 5.3 Bayesian Zero‐failure Test Plan for Substantiation Testing -- 5.4 Bayesian Zero‐failure Test Plan for Reliability Testing -- 5.5 Summary -- References -- Chapter 6 Capability and Design for Reliability -- 6.1 Introduction -- 6.2 Monte Caro Simulations with Parameter Point Estimates -- 6.2.1 Stress‐strength Interference Example.

6.2.2 Tolerance Stack‐up Example -- 6.3 Nested Monte Carlo Simulations with Bayesian Parameter Estimation -- 6.3.1 Stress‐strength Interference Example -- 6.3.2 Tolerance Stack‐up Example -- 6.4 Summary -- References -- Chapter 7 System Reliability Bayesian Model -- 7.1 Introduction -- 7.2 Reliability Block Diagram -- 7.3 Fault Tree -- 7.4 Bayesian Network -- 7.4.1 A Multiple‐sensor System -- 7.4.2 Dependent Failure Modes -- 7.4.3 Case Study: Aggregating Different Sources of Imperfect Data -- 7.5 Summary -- References -- Chapter 8 Bayesian Hierarchical Model -- 8.1 Introduction -- 8.2 Bayesian Hierarchical Binomial Model -- 8.2.1 Separate One‐level Bayesian Models -- 8.2.2 Bayesian Hierarchical Model -- 8.3 Bayesian Hierarchical Weibull Model -- 8.4 Summary -- References -- Chapter 9 Regression Models -- 9.1 Linear Regression -- 9.2 Binary Logistic Regression -- 9.3 Case Study: Defibrillation Efficacy Analysis -- 9.4 Summary -- References -- Appendix A Guidance for Installing R, R Studio, JAGS, and rjags -- A.1 Install R -- A.2 Install R Studio -- A.3 Install JAGS -- A.4 Install Package rjags -- A.5 Set Working Directory -- Appendix B Commonly Used R Commands -- B.1 How to Run R Commands -- B.2 General Commands -- B.3 Generate Data -- B.4 Variable Types -- B.5 Calculations and Operations -- B.6 Summarize Data -- B.7 Read and Write Data -- B.8 Plot Data -- B.9 Loops and Conditional Statements -- Appendix C Probability Distributions -- C.1 Discrete Distributions -- C.1.1 Binomial Distribution -- C.1.2 Poisson Distribution -- C.2 Continuous Distributions -- C.2.1 Beta Distribution -- C.2.2 Exponential Distribution -- C.2.3 Gamma Distribution -- C.2.4 Inverse Gamma Distribution -- C.2.5 Lognormal Distribution -- C.2.6 Normal Distribution -- C.2.7 Uniform Distribution -- C.2.8 Weibull Distribution -- Appendix D Jeffreys Prior -- Index -- EULA.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.