Overview
- Quantile functions provide a unique, unprecedentedly simple, robust, and precise approach to reliability theory
- Broad applicability across fields such as statistics, survival analysis, economics, engineering, demography, insurance, and medical science
- Clear presentation with many examples, figures, and tables
- Includes supplementary material: sn.pub/extras
Part of the book series: Statistics for Industry and Technology (SIT)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
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Quantile-Based Reliability Analysis’s innovative methodology is laid out in a well-organized sequence of topics, including:
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·      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.
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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.
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Reviews
From the book reviews:
“This book introduces quantile-based reliability analysis. It gives a novel approach to reliability theory using quantile functions in contrast to the traditional approach based on distribution functions. … This book has a broad applicability across fields such as statistics, survival analysis, economics, engineering, demography, insurance, and medical science. It can be used as an excellent reference book for faculty and professionals.” (Yuehua Wu, zbMATH 1306.62019, 2015)
“The reviewer finds it to be a good and quite exhaustive collection of results that are centered around quantile-based notions involving life distributions. Any researcher in the areas of probabilistic or statistical reliability theory may find this monograph to be a useful reference book.” (Moshe Shaked, Mathematical Reviews, April, 2014)Authors and Affiliations
Bibliographic Information
Book Title: Quantile-Based Reliability Analysis
Authors: N. Unnikrishnan Nair, P.G. Sankaran, N. Balakrishnan
Series Title: Statistics for Industry and Technology
DOI: https://doi.org/10.1007/978-0-8176-8361-0
Publisher: Birkhäuser New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2013
Hardcover ISBN: 978-0-8176-8360-3Published: 24 August 2013
Softcover ISBN: 978-1-4939-5167-3Published: 23 August 2016
eBook ISBN: 978-0-8176-8361-0Published: 24 August 2013
Series ISSN: 2364-6241
Series E-ISSN: 2364-625X
Edition Number: 1
Number of Pages: XX, 397
Number of Illustrations: 17 b/w illustrations, 3 illustrations in colour
Topics: Statistical Theory and Methods, Probability Theory and Stochastic Processes, Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences, Statistics for Business, Management, Economics, Finance, Insurance, Statistics for Life Sciences, Medicine, Health Sciences, Mathematical Modeling and Industrial Mathematics