E-Book Overview
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.
E-Book Content
Statistics for Industry and Technology
N. Unnikrishnan Nair P.G. Sankaran N. Balakrishnan
QuantileBased Reliability Analysis
Statistics for Industry and Technology Series Editor N. Balakrishnan McMaster University Hamilton, ON Canada
Editorial Advisory Board Max Engelhardt EG&G Idaho, Inc. Idaho Falls, ID, USA Harry F. Martz Los Alamos National Laboratory Los Alamos, NM, USA Gary C. McDonald NAO Research & Development Center Warren, MI, USA Kazuyuki Suzuki University of Electro Communications Chofu-shi, Tokyo Japan
For further volumes: http://www.springer.com/series/4982
N. Unnikrishnan Nair • P.G. Sankaran N. Balakrishnan
Quantile-Based Reliability Analysis
N. Unnikrishnan Nair Department of Statistics Cochin University of Science and Technology Cochin, Kerala, India
P.G. Sankaran Department of Statistics Cochin University of Science and Technology Cochin, Kerala, India
N. Balakrishnan Department of Mathematics and Statistics McMasters University Hamilton, ON, Canada
ISBN 978-0-8176-8360-3 ISBN 978-0-8176-8361-0 (eBook) DOI 10.1007/978-0-8176-8361-0 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2013943270 Mathematics Subject Classification (2010): 62E-XX, 62N05, 62P30 © Springer Science+Business Media New York 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive