Statistics for Industry and Technology

Quantile-Based Reliability Analysis

Authors: Nair, N. Unnikrishnan, Sankaran, P.G., Balakrishnan, N

  • 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
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Hardcover $79.95
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  • ISBN 978-0-8176-8360-3
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  • ISBN 978-1-4939-5167-3
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About this Textbook

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.

 

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)

Table of contents (9 chapters)

  • Quantile Functions

    Nair, N. Unnikrishnan (et al.)

    Pages 1-28

  • Quantile-Based Reliability Concepts

    Nair, N. Unnikrishnan (et al.)

    Pages 29-58

  • Quantile Function Models

    Nair, N. Unnikrishnan (et al.)

    Pages 59-103

  • Ageing Concepts

    Nair, N. Unnikrishnan (et al.)

    Pages 105-165

  • Total Time on Test Transforms

    Nair, N. Unnikrishnan (et al.)

    Pages 167-198

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-0-8176-8361-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-0-8176-8360-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.95
price for USA
  • ISBN 978-1-4939-5167-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Quantile-Based Reliability Analysis
Authors
Series Title
Statistics for Industry and Technology
Copyright
2013
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
Distribution Rights
Distribution rights for India: Delhi Book Store, New Delhi, India
eBook ISBN
978-0-8176-8361-0
DOI
10.1007/978-0-8176-8361-0
Hardcover ISBN
978-0-8176-8360-3
Softcover ISBN
978-1-4939-5167-3
Series ISSN
2364-6241
Edition Number
1
Number of Pages
XX, 397
Number of Illustrations and Tables
17 b/w illustrations, 3 illustrations in colour
Topics