Cover image

Title page

Copyright

Dedication

Authors Biographies

Preface

About the Book

Chapter 1: Reliability Theory

Abstract

1.1. Reliability Theory

1.2. Discrete Life Distributions

1.3. Mixture Distributions

1.4. Weighted Distributions

1.5. Convolution

1.6. Shock Models

1.7. Convexity and Related Concepts

1.8. Multivariate Distributions

1.9. Multivariate Weighted Distributions

1.10. Dependence Measures and Concepts

1.11. Schur Convexity and Concavity

References

Chapter 2: Basic Reliability Concepts

Abstract

2.1. Introduction

2.2. Hazard Rate Function

2.3. Mean Residual Life

2.4. Variance Residual Life Function

2.5. Upper Partial Moments

2.6. Reversed Hazard Rate

2.7. Reversed Mean Residual Life

2.8. Reversed Variance Residual Life

2.9. Odds Function

2.10. Log-odds Functions and Rates

2.11. Mixture Distributions

2.12. Weighted Distributions

References

Chapter 3: Discrete Lifetime Models

Abstract

3.1. Introduction

3.2. Families of Distributions

3.3. Discrete Analogues of Continuous Distributions

3.4. Some Other Models

References

Chapter 4: Discrete Ageing Concepts

Abstract

4.1. Introduction

4.2. Stochastic Orders

4.3. Classes Based on Hazard Rate

4.4. Classes Based on Residual Life

4.5. Classes Based on Survival Function

4.6. Classes Based on Reliability Functions in Reversed Time

4.7. Ageing Properties for Weighted Distributions

4.8. Relative Ageing

References

Chapter 5: Bathtub Distributions

Abstract

5.1. Introduction

5.2. Definitions and Techniques for Identification of Bathtub Distributions

5.3. Models

5.4. Methods of Constructing Bathtub Models

5.5. Properties of BT Models

5.6. Other Forms of Non-monotonic Hazard Rates

References

Chapter 6: Multivariate Reliability Concepts

Abstract

6.1. Introduction

6.2. Multivariate Hazard Rate

6.3. Multivariate Mean Residual Life

6.4. Variance Residual Life Functions

6.5. Multivariate Reversed Hazard Rate

6.6. Reversed Mean Residual Life Function

6.7. Bivariate Reversed Variance Residual Life

6.8. Reliability Functions and Time Dependent Measures of Association

6.9. Reliability Functions of Equilibrium Distributions

References

Chapter 7: Multivariate Ageing Concepts

Abstract

7.1. Introduction

7.2. Multivariate Stochastic Orders

7.3. Multivariate No-ageing

7.4. Multivariate IHR Classes

7.5. Bayesian Approach to Ageing Classes

7.6. Multivariate Increasing Hazard Rate Average

7.7. New Better Than Used in Hazard Rate

7.8. Multivariate Decreasing Mean Residual Life

7.9. Decreasing Conditional Mean Residual Life

7.10. Bayesian Definition of DMRL Distributions

7.11. Multivariate New Better Than Used Class

7.12. Multivariate New Better Than Used in Expectation

7.13. Multivariate Harmonic New Better Than Used in Expectation

7.14. Increasing Product Moment Residual Life

References

Chapter 8: Multivariate Lifetime Models

Abstract

8.1. Introduction

8.2. Multivariate Geometric Distributions

8.3. Schur-Constant Family

8.4. Bivariate Waring Distribution-1

8.5. Bivariate Waring Distribution-2

8.6. Bivariate Negative Hypergeometric Distribution

8.7. Bivariate Weibull Distribution

8.8. Multivariate Zipf Distributions

References

Chapter 9: Applications

Abstract

9.1. Introduction

9.2. Survival Analysis

9.3. Social Sciences

9.4. Risk Analysis

9.5. Information Theory

9.6. Mathematics and Statistics

References

References

Index