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.

YAN LIU, PHD, is Principal Reliability Engineer at Medtronic PLC, (USA). She is a certified Master Black Belt at Medtronic and has 12 years of working and consulting experience on reliability engineering and design for Six Sigma.

ATHULA I. ABEYRATNE, PHD, is Senior Principal Statistician and a certified DRM Black Belt at Medtronic PLC, (USA), where he has provided statistical consulting, training, data analyses, and modelling for 27 years.

Klappentext

PRACTICAL APPLICATIONS OF BAYESIAN RELIABILITY

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 then presented, followed by Bayesian computation, Metropolis-Hastings algorithm, and Gibbs Sampling. The book then goes on to cover concepts of design capability and design for reliability; introduction of Bayesian models for estimating system reliability; a discussion of Bayesian Hierarchical Models and their applications; and a presentation of linear and logistic regression models in Bayesian Perspective.

• 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.

Inhalt

Preface xi

Acknowledgments xv

About the Companion Website xvii

1 Basic Concepts of Reliability Engineering 1

1.1 Introduction 1

1.1.1 Reliability Definition 3

1.1.2 Design for Reliability and Design for Six Sigma 4

1.2 Basic Theory and Concepts of Reliability Statistics 5

1.2.1 Random Variables 5

1.2.2 Discrete Probability Distributions 6

1.2.3 Continuous Probability Distributions 6

1.2.4 Properties of Discrete and Continuous Random Variables 6

1.2.4.1 Probability Mass Function 6

1.2.4.2 Probability Density Function 7

1.2.4.3 Cumulative Distribution Function 8

1.2.4.4 Reliability or Survival Function 8

1.2.4.5 Hazard Rate or Instantaneous Failure Rate 9

1.2.4.6 Cumulative Hazard Function 10

1.2.4.7 The Average Failure Rate Over Time 10

1.2.4.8 Mean Time to Failure 10

1.2.4.9 Mean Number of Failures 11

1.2.5 Censored Data 11

1.2.6 Parametric Models of Time to Failure Data 13

1.2.7 Nonparametric Estimation of Survival 14

1.2.8 Accelerated Life Testing 16

1.3 Bayesian Approach to Reliability Inferences 18

1.3.1 Brief History of Bayes' Theorem and Bayesian Statistics 18

1.3.2 How Does Bayesian Statistics Relate to Other Advances in the Industry? 19

1.3.2.1 Advancement of Predictive Analytics 20

1.3.2.2 Cost Reduction 20

1.4 Component Reliability Estimation 20

1.5 System Reliability Estimation 20

1.6 Design Capability Prediction (Monte Carlo Simulations) 21

1.7 Summary 22

References 23

2 Basic Concepts of Bayesian Statistics and Models 25

2.1 Basic Idea of Bayesian Reasoning 25

2.2 Basic Probability Theory and Bayes' Theorem 26

2.3 Bayesian Inference (Point and Interval Estimation) 32

2.4 Selection of Prior Distributions 35

2.4.1 Conjugate Priors 35

2.4.2 Informative and Non-informative Priors 38

2.5 Bayesian Inference vs. Frequentist Inference 44

2.6 How Bayesian Inference Works with Monte Carlo Simulations 48

2.7 Bayes Factor and its Applications 50

2.8 Predictive Distribution 53

2.9 Summary 57

References 57

3 Bayesian Computation 59

3.1 Introduction 59

3.2 Discretization 60

3.3 Markov Chain Monte Carlo Algorithms 66

3.3.1 Markov Chains 67

3.3.1.1 Monte Car…