Quality Management and Operations Research: Understanding and Implementing the Nonparametric Bayesian Approach

Description

Offering a step-by-step approach for applying the Nonparametric Method with the Bayesian Approach to model complex relationships occurring in Reliability Engineering, Quality Management, and Operations Research, it also discusses survival and censored data, accelerated lifetime tests (issues in reliability data analysis), and R codes. This book uses the Nonparametric Bayesian approach in the fields of quality management and operations research. It presents a step-by-step approach for understanding and implementing these models, as well as includes R codes which can be used in any dataset. The book helps the readers to use statistical models in studying complex concepts and applying them to Operations Research, Industrial Engineering, Manufacturing Engineering, Computer Science, Quality and Reliability, Maintenance Planning and Operations Management. This book helps researchers, analysts, investigators, designers, producers, industrialists, entrepreneurs, and financial market decision makers, with finding the lifetime model of products, and for crucial decision-making in other markets. Cover Half Title Title Page Copyright Page Dedication Table of Contents Foreword Preface Acknowledgments Authors Chapter 1 Introduction 1.1 Need for Quality 1.2 Quality Management 1.2.1 Quality Management Parameters 1.3 Quality Determinants 1.4 Factors Affecting Reliability Chapter 2 Quality and Reliability 2.1 Some Remarkable Properties of Survival Data 2.2 Important Functions for Assessing Failure Time 2.2.1 Cumulative Distribution Function 2.2.2 Probability Density Function 2.2.3 Survival Function 2.2.4 Hazard Function 2.2.5 Quantile Function 2.3 Censor 2.4 Accelerated Lifetime Tests 2.4.1 Accelerated Lifetime Tests Models 2.4.2 Lifetime-Stress Relationship 2.5 Bayesian Approach 2.6 Markov Chain Monte Carlo Method 2.6.1 Monte Carlo Approach 2.6.1.1 Monte Carlo Integration 2.6.1.2 Importance Sampling 2.6.2 Markov Chain 2.6.2.1 Definitions 2.6.2.2 Chain Structure 2.6.2.3 Limiting Distribution of Chain 2.6.3 Metropolis–Hastings Algorithm 2.6.3.1 Gibbs Sampling Method 2.6.3.2 Some Features of the Gibbs Sampling Method 2.7 Slice Sampling Chapter 3 Dirichlet Process 3.1 Dirichlet Distribution 3.1.1 Remarkable Properties of the Dirichlet Distribution 3.2 Dirichlet Process 3.3 Pólya’s Urn Model 3.3.1 Pólya’s Urn Process 3.3.2 Blackwell–MacQueen Urn Scheme 3.4 Dirichlet Process and Clustering Issue 3.4.1 Chinese Restaurant Process Chapter 4 Nonparametric Bayesian Approach in Accelerated Lifetime Tests 4.1 Dirichlet Process Mixture Models 4.1.1 Mixture Models 4.2 Log-linear Regression in the Nonparametric Problem 4.3 Determining the Base Distribution and the Precision Parameter 4.4 Hierarchical Model of the Dirichlet Process 4.5 Bayesian Computation 4.6 Model Fitting 4.6.1 First Stage: Updating Θi[sub(i)] 4.6.2 Second Stage: Updating Θi[sub(j)] [sup(*)] 4.6.3 Third Stage: Updating ξ 4.6.4 Fourth Stage: Updating ß 4.6.5 Fifth Stage: Updating the Distribution of Failure-Time Chapter 5 Illustrative Examples and Results 5.1 E mpirical Distribution Function 5.2 Dirichlet Process Weibull Mixture Model 5.2.1 De termining Base Distribution 5.3 A ssessing the Model and Simulation 5.3.1 Updating (α[sub(i)] , λ[sub(i)]) 5.3.2 Updating (α[sub(j)][sup(*)] , λ[sub(j)][sup(*)]) 5.3.3 Updating Ø, γ, and μ 5.3.3.1 Updating Ø 5.3.3.2 Updating γ 5.3.3.3 Updating μ 5.3.3.4 Updating β 5.4 I llustrative Examples Appendix A: Guide to Proofs Appendix B: R Programming Codes References Index