Practical Applications of Bayesian Reliability

Book description

Demonstrates how to solve reliability problems using practical applications of Bayesian models

This self-contained reference provides fundamental knowledge of Bayesian reliability and utilizes numerous examples to show how Bayesian models can solve real life reliability problems. It teaches engineers and scientists exactly what Bayesian analysis is, what its benefits are, and how they can apply the methods to solve their own problems. To help readers get started quickly, the book presents many Bayesian models that use JAGS and which require fewer than 10 lines of command. It also offers a number of short R scripts consisting of simple functions to help them become familiar with R coding.

Practical Applications of Bayesian Reliability starts by introducing basic concepts of reliability engineering, including random variables, discrete and continuous probability distributions, hazard function, and censored data. Basic concepts of Bayesian statistics, models, reasons, and theory are presented in the following chapter. Coverage of Bayesian computation, Metropolis-Hastings algorithm, and Gibbs Sampling comes next. The book then goes on to teach the concepts of design capability and design for reliability; introduce Bayesian models for estimating system reliability; discuss Bayesian Hierarchical Models and their applications; present linear and logistic regression models in Bayesian Perspective; and more. 

  • Provides a step-by-step approach for developing advanced reliability models to solve complex problems, and does not require in-depth understanding of statistical methodology
  • Educates managers on the potential of Bayesian reliability models and associated impact
  • Introduces commonly used predictive reliability models and advanced Bayesian models based on real life applications
  • Includes practical guidelines to construct Bayesian reliability models along with computer codes for all of the case studies
  • JAGS and R codes are provided on an accompanying website to enable practitioners to easily copy them and tailor them to their own applications 

Practical Applications of Bayesian Reliability is a helpful book for industry practitioners such as reliability engineers, mechanical engineers, electrical engineers, product engineers, system engineers, and materials scientists whose work includes predicting design or product performance. 

Table of contents

  1. Cover
  2. Preface
  3. Acknowledgments
  4. About the Companion Website
  5. 1 Basic Concepts of Reliability Engineering
    1. 1.1 Introduction
    2. 1.2 Basic Theory and Concepts of Reliability Statistics
    3. 1.3 Bayesian Approach to Reliability Inferences
    4. 1.4 Component Reliability Estimation
    5. 1.5 System Reliability Estimation
    6. 1.6 Design Capability Prediction (Monte Carlo Simulations)
    7. 1.7 Summary
    8. References
  6. 2 Basic Concepts of Bayesian Statistics and Models
    1. 2.1 Basic Idea of Bayesian Reasoning
    2. 2.2 Basic Probability Theory and Bayes' Theorem
    3. 2.3 Bayesian Inference (Point and Interval Estimation)
    4. 2.4 Selection of Prior Distributions
    5. 2.5 Bayesian Inference vs. Frequentist Inference
    6. 2.6 How Bayesian Inference Works with Monte Carlo Simulations
    7. 2.7 Bayes Factor and its Applications
    8. 2.8 Predictive Distribution
    9. 2.9 Summary
    10. References
  7. 3 Bayesian Computation
    1. 3.1 Introduction
    2. 3.2 Discretization
    3. 3.3 Markov Chain Monte Carlo Algorithms
    4. 3.4 Using BUGS/JAGS
    5. 3.5 Summary
    6. References
  8. 4 Reliability Distributions (Bayesian Perspective)
    1. 4.1 Introduction
    2. 4.2 Discrete Probability Models
    3. 4.3 Continuous Models
    4. 4.4 Model and Convergence Diagnostics
    5. References
  9. 5 Reliability Demonstration Testing
    1. 5.1 Classical Zero‐failure Test Plans for Substantiation Testing
    2. 5.2 Classical Zero‐failure Test Plans for Reliability Testing
    3. 5.3 Bayesian Zero‐failure Test Plan for Substantiation Testing
    4. 5.4 Bayesian Zero‐failure Test Plan for Reliability Testing
    5. 5.5 Summary
    6. References
  10. 6 Capability and Design for Reliability
    1. 6.1 Introduction
    2. 6.2 Monte Caro Simulations with Parameter Point Estimates
    3. 6.3 Nested Monte Carlo Simulations with Bayesian Parameter Estimation
    4. 6.4 Summary
    5. References
  11. 7 System Reliability Bayesian Model
    1. 7.1 Introduction
    2. 7.2 Reliability Block Diagram
    3. 7.3 Fault Tree
    4. 7.4 Bayesian Network
    5. 7.5 Summary
    6. References
  12. 8 Bayesian Hierarchical Model
    1. 8.1 Introduction
    2. 8.2 Bayesian Hierarchical Binomial Model
    3. 8.3 Bayesian Hierarchical Weibull Model
    4. 8.4 Summary
    5. References
  13. 9 Regression Models
    1. 9.1 Linear Regression
    2. 9.2 Binary Logistic Regression
    3. 9.3 Case Study: Defibrillation Efficacy Analysis
    4. 9.4 Summary
    5. References
  14. Appendix A: Guidance for Installing R, R Studio, JAGS, and rjags
    1. A.1 Install R
    2. A.2 Install R Studio
    3. A.3 Install JAGS
    4. A.4 Install Package rjags
    5. A.5 Set Working Directory
  15. Appendix B: Commonly Used R Commands
    1. B.1 How to Run R Commands
    2. B.2 General Commands
    3. B.3 Generate Data
    4. B.4 Variable Types
    5. B.5 Calculations and Operations
    6. B.6 Summarize Data
    7. B.7 Read and Write Data
    8. B.8 Plot Data
    9. B.9 Loops and Conditional Statements
  16. Appendix C: Probability Distributions
    1. Discrete Distributions
    2. Continuous Distributions
  17. Appendix D: Jeffreys Prior
  18. Index
  19. End User License Agreement

Product information

  • Title: Practical Applications of Bayesian Reliability
  • Author(s): Yan Liu, Athula I. Abeyratne
  • Release date: May 2019
  • Publisher(s): Wiley
  • ISBN: 9781119287971