Quantile-based reliability analysis
type: Item
instance of: scholarly article
title: Quantile-based reliability analysis
zbMATH Open document ID: 1306.62019
DOI: 10.1007/978-0-8176-8361-0
published in: Statistics for Industry and Technology
publication date: 2013-06-18T00:00:00Z
review text: 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. Even though quantile functions and distribution functions are mathematically equivalent ways to define a probability distribution, the book shows that quantile functions have several advantages over distribution functions: (1) many data sets with non-elementary distribution functions can be modeled by quantile functions with simple forms; (2) most quantile functions approximate many of the standard models in reliability analysis quite well, and hence an arbitrary quantile function will be a good first approximation if physical conditions do not suggest a plausible model; (3) the inference procedures for quantile models need less information and are more robust to outliers. By the way, the book is written or as said in its preface, the book is biased towards the mathematical theory, with examples intended to clarify various notions and applications to real data being limited to demonstrate the utility of quantile functions. This book has nine chapters. Chapter 1 deals with the definition, properties and various descriptive measures based on the quantile functions including order statistics and \(L\)-moments, and demonstrates some graphic methods. Chapter 2 discusses various reliability concepts like hazard rate, and mean residual life, in the conventional form as well as their quantile equivalents. Chapter 3 gives a detailed presentation of the distributional and reliability aspects of quantile function models along with some applications to real data. Chapter 4 describes different aging concepts in quantile versions. Chapter 5 covers total time on test transforms, an essentially quantile-based notion in details. Chapter 6 discusses the \(L\)-moments and partial moments in relation to residual life along with their use in inferential methods, which are alternatives t…
Mathematics Subject Classification ID: 62-01
Mathematics Subject Classification ID: 62P30
Mathematics Subject Classification ID: 62N05
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 6176764
author: N. Unnikrishnan Nair
author: P. G. Sankaran
author: Narayanaswamy Balakrishnan
reviewed by: Yuehua Wu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-0-8176-8361-0
OpenAlex ID: W4230880328
description: scientific article; zbMATH DE number 6176764