Practical Applications of Bayesian Reliability

Yan Liu, Athula I. Abeyratne

• Publisher: Wiley
• Year: 2019
• Print ISBN: 9781119287971
• eBook ISBN: 9781119287988
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Quality Control in Engineering
• Index: Technology & Engineering

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.

1
Basic Concepts of Reliability Engineering

This chapter reviews basic concepts and common reliability engineering practices in the manufacturing industry. In addition, we briefly introduce the history of Bayesian statistics and how it relates to advances in the field of reliability engineering.

Experienced reliability engineers who are very familiar with reliability basics and would like to start learning Bayesian statistics right away, may skip this chapter and start with Chapter 2. Bayesian statistics has unique advantages for reliability estimations and predictive analytics in complex systems. In other cases, Bayesian methods may provide flexible solutions to aggregate various sources of information to potentially reduce necessary sample sizes and therefore achieve cost effectiveness. The following chapters provide more specific discussions and case study examples to expand on these topics.

1.1 Introduction

High product quality and reliability are critical to any industry in today's competitive business environment. In addition, predictable development time, efficient manufacturing with high yields, and exemplary field reliability are all hallmarks of a successful product development process.

Some of the popular best practices in industry include Design for Reliability and Design for Six Sigma programs to improve product robustness during the design phase. One core competency in these programs is to adopt advanced predictive analytics early in the product development to ensure first‐pass success, instead of over‐reliance on physical testing at the end of the development phase or on field performance data after product release.

The International Organization for Standardization (ISO) defines reliability as the “ability of a structure or structural member to fulfil the specified requirements, during the working life, for which it has been designed” (ISO 2394:2015 General principles on reliability for structures, Section 2.1.8). Typically, reliability is stated in terms of probability and associated confidence level. As an example, the reliability of a light bulb can be stated as the probability that the light bulb will last 5000 hours under normal operating conditions is 0.95 with 95% confidence.

Accurate and timely reliability prediction during the product development phase provides inputs for the design strategy and boosts understanding and confidence in product reliability before products are released to the market. It is also desirable to utilize and aggregate information from different sources in an effective way for reliability predictions.

Textbooks on reliability engineering nowadays are dominated by frequentist statistics approaches for reliability modeling and predictions. In a frequentist/classical framework, it is often difficult or impossible to propagate individual component level classical confidence intervals to a complex system comprising many components or subsystems. In a Bayesian framework, on the other hand, posterior distributions are true probability statements about unknown parameters, so they may be easily propagated through these system reliability models. Besides, it is often more flexible to use Bayesian models to integrate different sources of information, and update inferences when new data becomes available.

Given the benefits mentioned above, potential applications of Bayesian methods on reliability prediction are quite extensive. Historically, Bayesian methods for reliability engineering were applied on component reliability assessment where conjugate prior (will be discussed in Chapter 2) distributions were widely used due to mathematical tractability. Recent breakthroughs in computational algorithms have made it feasible to solve more complex Bayesian...

Table of contents

• Cover
• Table of Contents
• Preface
• Acknowledgments
• About the Companion Website
• 1 Basic Concepts of Reliability Engineering
• 2 Basic Concepts of Bayesian Statistics and Models
• 3 Bayesian Computation
• 4 Reliability Distributions (Bayesian Perspective)
• 5 Reliability Demonstration Testing
• 6 Capability and Design for Reliability
• 7 System Reliability Bayesian Model
• 8 Bayesian Hierarchical Model
• 9 Regression Models
• Appendix A: Guidance for Installing R, R Studio, JAGS, and rjags
• Appendix B: Commonly Used R Commands
• Appendix C: Probability Distributions
• Appendix D: Jeffreys Prior
• Index
• End User License Agreement