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.




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.




Bayesian Reliability


Book Description

Bayesian Reliability presents modern methods and techniques for analyzing reliability data from a Bayesian perspective. The adoption and application of Bayesian methods in virtually all branches of science and engineering have significantly increased over the past few decades. This increase is largely due to advances in simulation-based computational tools for implementing Bayesian methods. The authors extensively use such tools throughout this book, focusing on assessing the reliability of components and systems with particular attention to hierarchical models and models incorporating explanatory variables. Such models include failure time regression models, accelerated testing models, and degradation models. The authors pay special attention to Bayesian goodness-of-fit testing, model validation, reliability test design, and assurance test planning. Throughout the book, the authors use Markov chain Monte Carlo (MCMC) algorithms for implementing Bayesian analyses -- algorithms that make the Bayesian approach to reliability computationally feasible and conceptually straightforward. This book is primarily a reference collection of modern Bayesian methods in reliability for use by reliability practitioners. There are more than 70 illustrative examples, most of which utilize real-world data. This book can also be used as a textbook for a course in reliability and contains more than 160 exercises. Noteworthy highlights of the book include Bayesian approaches for the following: Goodness-of-fit and model selection methods Hierarchical models for reliability estimation Fault tree analysis methodology that supports data acquisition at all levels in the tree Bayesian networks in reliability analysis Analysis of failure count and failure time data collected from repairable systems, and the assessment of various related performance criteria Analysis of nondestructive and destructive degradation data Optimal design of reliability experiments Hierarchical reliability assurance testing




Bayesian Networks for Reliability Engineering


Book Description

This book presents a bibliographical review of the use of Bayesian networks in reliability over the last decade. Bayesian network (BN) is considered to be one of the most powerful models in probabilistic knowledge representation and inference, and it is increasingly used in the field of reliability. After focusing on the engineering systems, the book subsequently discusses twelve important issues in the BN-based reliability methodologies, such as BN structure modeling, BN parameter modeling, BN inference, validation, and verification. As such, it is a valuable resource for researchers and practitioners in the field of reliability engineering.




Risk and Reliability Analysis: Theory and Applications


Book Description

This book presents a unique collection of contributions from some of the foremost scholars in the field of risk and reliability analysis. Combining the most advanced analysis techniques with practical applications, it is one of the most comprehensive and up-to-date books available on risk-based engineering. All the fundamental concepts needed to conduct risk and reliability assessments are covered in detail, providing readers with a sound understanding of the field and making the book a powerful tool for students and researchers alike. This book was prepared in honor of Professor Armen Der Kiureghian, one of the fathers of modern risk and reliability analysis.




System and Bayesian Reliability


Book Description

This volume is a collection of articles on reliability systems and Bayesian reliability analysis. Written by reputable researchers, the articles are self-contained and are linked with literature reviews and new research ideas. The book is dedicated to Emeritus Professor Richard E Barlow, who is well known for his pioneering research on reliability theory and Bayesian reliability analysis. Contents: System Reliability Analysis: On Regular Reliability Models (J-C Chang et al.); Bounding System Reliability (J N Hagstrom & S M Ross); Large Excesses for Finite-State Markov Chains (D Blackwell); Ageing Properties: Nonmonotonic Failure Rates and Mean Residual Life Functions (R C Gupta); The Failure Rate and the Mean Residual Lifetime of Mixtures (M S Finkelstein); On Some Discrete Notions of Aging (C Bracquemond et al.); Bayesian Analysis: On the Practical Implementation of the Bayesian Paradigm in Reliability and Risk Analysis (T Aven); A Weibull Wearout Test: Full Bayesian Approach (T Z Irony et al.); Bayesian Nonparametric Estimation of a Monotone Hazard Rate (M-W Ho & A Y Lo); and other papers. Readership: Students, academics, researchers and professionals in industrial engineering, probability and statistics, and applied mathematics.




The Theory and Applications of Reliability With Emphasis on Bayesian and Nonparametric Methods


Book Description

The Theory and Applications of Reliability: With Emphasis on Bayesian and Nonparametric Methods, Volume I covers the proceedings of the conference on ""The Theory and Applications of Reliability with Emphasis on Bayesian and Nonparametric Methods."" The conference is organized so as to have technical presentations, a clinical session, and round table discussions. This volume is a 29-chapter text that specifically deals with the theoretical aspects of reliability estimation. Considerable chapters on the technical sessions are devoted to initial findings on the theory and applications of reliability estimation, with special emphasis on Bayesian and nonparametric methods. A Bayesian analysis implies the use of suitable prior information in association with Bayes theorem while the nonparametric approach analyzes the reliability components and systems under the assumption of a time-to-failure distribution with a wide defining property rather than a specific parametric class of probability distributions. The clinical session chapters discuss the actual problems encountered in reliability estimation. The remaining chapters deal with the status of the subject areas and the empirical Bayes developments. These chapters also present various probabilistic and statistic methods for reliability estimation. Theoreticians and reliability engineers will find this book invaluable.







Bayesian Methods in Reliability


Book Description

When data is collected on failure or survival a list of times is obtained. Some of the times are failure times and others are the times at which the subject left the experiment. These times both give information about the performance of the system. The two types will be referred to as failure and censoring times (cf. Smith section 5). * A censoring time, t, gives less information than a failure time, for it is * known only that the item survived past t and not when it failed. The data is tn and of censoring thus collected as a list of failure times t , . . . , l * * * times t , t , . . . , t • 1 z m 2. 2. Classical methods The failure times are assumed to follow a parametric distribution F(t;B) with and reliability R(t;B). There are several methods of estimating density f(t;B) the parameter B based only on the data in the sample without any prior assumptions about B. The availability of powerful computers and software packages has made the method of maximum likelihood the most popular. Descriptions of most methods can be found in the book by Mann, Schafer and Singpurwalla (1974). In general the method of maximum likelihood is the most useful of the classical approaches. The likelihood approach is based on constructing the joint probability distrilmtion or density for a sample.