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Quantile-Based Reliability Analysis

  • N. Unnikrishnan Nair
  • P.G. Sankaran
  • N. Balakrishnan

Part of the Statistics for Industry and Technology book series (SIT)

Table of contents

  1. Front Matter
    Pages i-xx
  2. N. Unnikrishnan Nair, P. G. Sankaran, N. Balakrishnan
    Pages 1-28
  3. N. Unnikrishnan Nair, P. G. Sankaran, N. Balakrishnan
    Pages 29-58
  4. N. Unnikrishnan Nair, P. G. Sankaran, N. Balakrishnan
    Pages 59-103
  5. N. Unnikrishnan Nair, P. G. Sankaran, N. Balakrishnan
    Pages 105-165
  6. N. Unnikrishnan Nair, P. G. Sankaran, N. Balakrishnan
    Pages 167-198
  7. N. Unnikrishnan Nair, P. G. Sankaran, N. Balakrishnan
    Pages 199-233
  8. N. Unnikrishnan Nair, P. G. Sankaran, N. Balakrishnan
    Pages 235-279
  9. N. Unnikrishnan Nair, P. G. Sankaran, N. Balakrishnan
    Pages 281-326
  10. N. Unnikrishnan Nair, P. G. Sankaran, N. Balakrishnan
    Pages 327-359
  11. Back Matter
    Pages 361-397

About this book

Introduction

Quantile-Based Reliability Analysis presents a novel approach to reliability theory using quantile functions in contrast to the traditional approach based on distribution functions. Quantile functions and distribution functions are mathematically equivalent ways to define a probability distribution. However, quantile functions have several advantages over distribution functions. First, many data sets with non-elementary distribution functions can be modeled by quantile functions with simple forms. Second, most quantile functions approximate many of the standard models in reliability analysis quite well. Consequently, if physical conditions do not suggest a plausible model, an arbitrary quantile function will be a good first approximation. Finally, the inference procedures for quantile models need less information and are more robust to outliers.

 

Quantile-Based Reliability Analysis’s innovative methodology is laid out in a well-organized sequence of topics, including:

 

·       Definitions and properties of reliability concepts in terms of quantile functions;

·       Ageing concepts and their interrelationships;

·       Total time on test transforms;

·       L-moments of residual life;

·       Score and tail exponent functions and relevant applications;

·       Modeling problems and stochastic orders connecting quantile-based reliability functions.

 

An ideal text for advanced undergraduate and graduate courses in reliability and statistics, Quantile-Based Reliability Analysis also contains many unique topics for study and research in survival analysis, engineering, economics, and the medical sciences. In addition, its illuminating discussion of the general theory of quantile functions is germane to many contexts involving statistical analysis.

 

Keywords

estimation and statistical modeling hazard and residual quantile functions lifetime distributions quantile functions reliability analysis

Authors and affiliations

  • N. Unnikrishnan Nair
    • 1
  • P.G. Sankaran
    • 2
  • N. Balakrishnan
    • 3
  1. 1.Department of StatisticsCochin University of Science and TechnolCochinIndia
  2. 2.Department of StatisticsCochin University of Science and TechnolCochinIndia
  3. 3.Department of Mathematics and Statistics McMaster UniversityHamiltonCanada

Bibliographic information