Cover image for Reliability Modelling and Analysis in Discrete Time

Reliability Modelling and Analysis in Discrete Time

Author N. Balakrishnan , P.G. Sankaran , Unnikrishnan Nair
Release Date: 2018/05/01
ISBN: 9780128020067
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Book Description

Reliability Modelling and Analysis in Discrete Time provides an overview of the probabilistic and statistical aspects connected with discrete reliability systems. This engaging book discusses their distributional properties and dependence structures before exploring various orderings associated between different reliability structures. Though clear explanations, multiple examples, and exhaustive coverage of the basic and advanced topics of research in this area, the work gives the reader a thorough understanding of the theory and concepts associated with discrete models and reliability structures. A comprehensive bibliography assists readers who are interested in further research and understanding.

Requiring only an introductory understanding of statistics, this book offers valuable insight and coverage for students and researchers in Probability and Statistics, Electrical Engineering, and Reliability/Quality Engineering. The book also includes a comprehensive bibliography to assist readers seeking to delve deeper.

  • Includes a valuable introduction to Reliability Theory before covering advanced topics of research and real world applications
  • Features an emphasis on the mathematical theory of reliability modeling
  • Provides many illustrative examples to foster reader understanding

Table of Contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. Dedication
  6. Authors Biographies
  7. Preface
  8. About the Book
  9. Chapter 1: Reliability Theory
    1. Abstract
    2. 1.1. Reliability Theory
    3. 1.2. Discrete Life Distributions
    4. 1.3. Mixture Distributions
    5. 1.4. Weighted Distributions
    6. 1.5. Convolution
    7. 1.6. Shock Models
    8. 1.7. Convexity and Related Concepts
    9. 1.8. Multivariate Distributions
    10. 1.9. Multivariate Weighted Distributions
    11. 1.10. Dependence Measures and Concepts
    12. 1.11. Schur Convexity and Concavity
    13. References
  10. Chapter 2: Basic Reliability Concepts
    1. Abstract
    2. 2.1. Introduction
    3. 2.2. Hazard Rate Function
    4. 2.3. Mean Residual Life
    5. 2.4. Variance Residual Life Function
    6. 2.5. Upper Partial Moments
    7. 2.6. Reversed Hazard Rate
    8. 2.7. Reversed Mean Residual Life
    9. 2.8. Reversed Variance Residual Life
    10. 2.9. Odds Function
    11. 2.10. Log-odds Functions and Rates
    12. 2.11. Mixture Distributions
    13. 2.12. Weighted Distributions
    14. References
  11. Chapter 3: Discrete Lifetime Models
    1. Abstract
    2. 3.1. Introduction
    3. 3.2. Families of Distributions
    4. 3.3. Discrete Analogues of Continuous Distributions
    5. 3.4. Some Other Models
    6. References
  12. Chapter 4: Discrete Ageing Concepts
    1. Abstract
    2. 4.1. Introduction
    3. 4.2. Stochastic Orders
    4. 4.3. Classes Based on Hazard Rate
    5. 4.4. Classes Based on Residual Life
    6. 4.5. Classes Based on Survival Function
    7. 4.6. Classes Based on Reliability Functions in Reversed Time
    8. 4.7. Ageing Properties for Weighted Distributions
    9. 4.8. Relative Ageing
    10. References
  13. Chapter 5: Bathtub Distributions
    1. Abstract
    2. 5.1. Introduction
    3. 5.2. Definitions and Techniques for Identification of Bathtub Distributions
    4. 5.3. Models
    5. 5.4. Methods of Constructing Bathtub Models
    6. 5.5. Properties of BT Models
    7. 5.6. Other Forms of Non-monotonic Hazard Rates
    8. References
  14. Chapter 6: Multivariate Reliability Concepts
    1. Abstract
    2. 6.1. Introduction
    3. 6.2. Multivariate Hazard Rate
    4. 6.3. Multivariate Mean Residual Life
    5. 6.4. Variance Residual Life Functions
    6. 6.5. Multivariate Reversed Hazard Rate
    7. 6.6. Reversed Mean Residual Life Function
    8. 6.7. Bivariate Reversed Variance Residual Life
    9. 6.8. Reliability Functions and Time Dependent Measures of Association
    10. 6.9. Reliability Functions of Equilibrium Distributions
    11. References
  15. Chapter 7: Multivariate Ageing Concepts
    1. Abstract
    2. 7.1. Introduction
    3. 7.2. Multivariate Stochastic Orders
    4. 7.3. Multivariate No-ageing
    5. 7.4. Multivariate IHR Classes
    6. 7.5. Bayesian Approach to Ageing Classes
    7. 7.6. Multivariate Increasing Hazard Rate Average
    8. 7.7. New Better Than Used in Hazard Rate
    9. 7.8. Multivariate Decreasing Mean Residual Life
    10. 7.9. Decreasing Conditional Mean Residual Life
    11. 7.10. Bayesian Definition of DMRL Distributions
    12. 7.11. Multivariate New Better Than Used Class
    13. 7.12. Multivariate New Better Than Used in Expectation
    14. 7.13. Multivariate Harmonic New Better Than Used in Expectation
    15. 7.14. Increasing Product Moment Residual Life
    16. References
  16. Chapter 8: Multivariate Lifetime Models
    1. Abstract
    2. 8.1. Introduction
    3. 8.2. Multivariate Geometric Distributions
    4. 8.3. Schur-Constant Family
    5. 8.4. Bivariate Waring Distribution-1
    6. 8.5. Bivariate Waring Distribution-2
    7. 8.6. Bivariate Negative Hypergeometric Distribution
    8. 8.7. Bivariate Weibull Distribution
    9. 8.8. Multivariate Zipf Distributions
    10. References
  17. Chapter 9: Applications
    1. Abstract
    2. 9.1. Introduction
    3. 9.2. Survival Analysis
    4. 9.3. Social Sciences
    5. 9.4. Risk Analysis
    6. 9.5. Information Theory
    7. 9.6. Mathematics and Statistics
    8. References
  18. References
  19. Index
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