Reliability Modelling with Information Measures

The book deals with the application of various measures of information like the entropy, divergence, inaccuracy, etc. in modelling lifetimes of devices or equipment in reliability analysis. This is an emerging area of study and research during the last two decades and is of potential interest in many fields. In this work the classical measures of uncertainty are sufficiently modified to meet the needs of lifetime data analysis. The book provides an exhaustive collection of materials in a single volume to make it a comprehensive source of reference. The first treatise on the subject. It brings together the work that have appeared in journals on different disciplines. It will serve as a text for graduate students and practioners of special studies in information theory, as well as statistics and as a reference book for researchers. The book contains illustrative examples, tables and figures for clarifying the concepts and methodologies, the book is self-contained. It helps students to access information relevant to careers in industry, engineering, applied statistics, etc. The book deals with the application of various measures of information like the entropy, divergence, inaccuracy, etc. in modelling lifetimes of devices or equipment in reliability analysis. Cover 1 Title Page 2 Copyright Page 3 Preface 4 Table of Contents 6 1. Preliminaries 10 1.1 Reliability analysis and information theory 10 1.2 Basic reliability functions 12 1.3 Quantile-based reliability functions 19 1.4 Quantile function models 23 1.5 Ageing and associated criteria 26 1.6 Concepts based on hazard rate 27 1.7 Concepts based on residual life 30 1.8 Classes based on survival function 32 1.9 Concepts in reversed time 34 1.10 Order statistics 35 1.11 Log concave and convex distributions 37 1.12 Weighted distributions 39 1.13 Stochastic orders 43 2. Residual Entropy 49 2.1 Introduction 49 2.2 Definition and properties of entropy 50 2.3 Differential entropy 53 2.4 Residual entropy 56 2.5 Order statistics 67 2.6 Quantile-based residual entropy 71 2.7 Weighted residual entropy 87 2.8 Stochastic orders 90 2.9 Estimation and testing 95 2.10 Residual extropy 100 3. Entropy of Past Life 111 3.1 Past entropy 111 3.2 Properties of past entropy 113 3.3 Past quantile entropy 129 3.4 Order statistics 135 3.5 Weighted past entropy 139 3.6 Interval entropy 142 3.7 Past extropy 144 4. Generalized Entropies 152 4.1 Introduction 152 4.2 Renyi entropy 153 4.3 Tsallis entropy 178 4.4 Varma entropy 185 4.5 Other entropies 188 5. Divergence Measures 190 5.1 Introduction 190 5.2 Kullback-Leibler divergence 191 5.3 Renyi’s divergence 207 5.4 Varma divergence 214 5.5 Csiszar’s family 215 5.6 Chernoff distance 218 5.7 Lin-Wong divergence 219 6. Inaccuracy 221 6.1 Introduction 221 6.2 Inaccuracy of residual lives 222 6.3 Quantile-based inaccuracy 236 6.4 Past inaccuracy measure 243 6.5 Estimation 245 7. Cumulative Entropy 248 7.1 Introduction 248 7.2 Cumulative entropy of residual life 251 7.3 Cumulative residual entropy of order n 258 7.4 Dynamic version of Cn 262 7.5 Weighted cumulative residual entropy 269 7.6 Cumulative entropy 274 7.7 Quantile-based cumulative entropy 277 7.8 Other topics 285 8. Generalized Cumulative Entropy and Divergence 289 8.1 Introduction 289 8.2 Survival and failure entropies 289 8.3 Cumulative divergence 296 8.4 Cumulative Tsallis entropy 301 8.5 Cumulative Varma’s entropy 309 8.6 Cumulative residual inaccuracy 311 8.7 Generalized cumulative residual entropy 316 References 328 Index 352 proportional,hazard,models;,generalized,cumulative,entropy,and,divergence;,divergence,Measures;,residual,and,past,entropies;,Entropy proportional hazard models,generalized cumulative entropy and divergence,divergence Measures,residual and past entropies,Entropy "This is the first book on this topic and has no competing works in literature. so that there may not be any market competition. The interface between Information Theory and Reliability is only two decades old and continues to be a fertile area for study and research. The topic has attracted several researchers from statistics, reliability and survival analysis, industry, communications and engineering. There is no single source for finding the literature spread over several journals and the book meets this demand. This book can be used as textbook for specialization in statistics and communication courses. It serves also as a self-contained reference volume"-- Provided by publisher