scispace - formally typeset
Search or ask a question
Book

Statistical Theory of Reliability and Life Testing: Probability Models

TL;DR: A number of new classes of life distributions arising naturally in reliability models are treated systematically and each provides a realistic probabilistic description of a physical property occurring in the reliability context, thus permitting more realistic modeling of commonly occurring reliability situations.
Abstract: : This is the first of two books on the statistical theory of reliability and life testing. The present book concentrates on probabilistic aspects of reliability theory, while the forthcoming book will focus on inferential aspects of reliability and life testing, applying the probabilistic tools developed in this volume. This book emphasizes the newer, research aspects of reliability theory. The concept of a coherent system serves as a unifying theme for much of the book. A number of new classes of life distributions arising naturally in reliability models are treated systematically: the increasing failure rate average, new better than used, decreasing mean residual life, and other classes of distributions. As the names would seem to indicate, each such class of life distributions provides a realistic probabilistic description of a physical property occurring in the reliability context. Also various types of positive dependence among random variables are considered, thus permitting more realistic modeling of commonly occurring reliability situations.
Citations
More filters
Book
Ove Ditlevsen, H. O. Madsen1
01 Jun 1996
TL;DR: Partial Safety Factor Method Probabilistic Information Simple Reliability Index Geometricreliability Index Generalized Reliability index Transformation Sensitivity Analysis Monte Carlo Methods Load Combinations Statistical and Model Uncertainty Decision Philosophy Reliability of Existing Structures System Reliability Analysis.
Abstract: Partial Safety Factor Method Probabilistic Information Simple Reliability Index Geometric Reliability Index Generalized Reliability Index Transformation Sensitivity Analysis Monte Carlo Methods Load Combinations Statistical and Model Uncertainty Decision Philosophy Reliability of Existing Structures System Reliability Analysis Introduction to Process Descriptions.

1,852 citations

Journal ArticleDOI
TL;DR: This paper provides a comprehensive review that synthesizes existing results for the single period problem and develops additional results to enrich the existing knowledge base, and reviews and develops insight into a dynamic inventory extension of this problem.
Abstract: In the newsvendor problem, a decision maker facing random demand for a perishable product decides how much of it to stock for a single selling period. This simple problem with its intuitively appealing solution is a crucial building block of stochastic inventory theory, which comprises a vast literature focusing on operational efficiency. Typically in this literature, market parameters such as demand and selling price are exogenous. However, incorporating these factors into the mode l can provide an excellent vehicle for examining how operational problems interact with marketing issues to influence decision making at the firm level. In this paper we examine an extension of the newsvendor problem in which stocking quantity and selling price are set simultaneously. We provide a comprehensive review that synthesizes existing results for the single period problem and develop additional results to enrich the existing knowledge base. We also review and develop insight into a dynamic inventory extension of this problem, and motivate the applicability of such models.

1,579 citations

Journal ArticleDOI
Hongzhou Wang1
TL;DR: This survey summarizes, classifies, and compares various existing maintenance policies for both single-unit and multi-unit systems, with emphasis on single- unit systems.

1,507 citations


Cites background or methods from "Statistical Theory of Reliability a..."

  • ...Detailed comparisons on the age and block replacement policies can be found in Barlow and Proshan (1965, 1975) in which the general conclusion is that the age replacement policy is an economical way to the block replacement policy....

    [...]

  • ...McCall (1963), Barlow and Proshan (1965, 1975), Pierskalla and Voelker (1976), Osaki and Nakagawa (1976), Sherif and Smith (1981), Jardine and Buzacott (1985), Valdez-Flores and Feldman (1989), Cho and Parlar *Fax: +1-732-949-0019....

    [...]

  • ...Hundreds of papers and models have been published (McCall (1963), Barlow and Proshan (1965, 1975), Pierskalla and Voelker (1976), Osaki and Nakagawa (1976), Sherif and Smith (1981), Jardine and Buzacott (1985), Valdez-Flores and Feldman (1989), Pham and Wang (1996)) under these two kinds of maintenance policies....

    [...]

  • ...McCall (1963), Barlow and Proshan (1965, 1975), Pierskalla and Voelker (1976), Osaki and Nakagawa (1976), Sherif and Smith (1981), Jardine and Buzacott (1985), Valdez-Flores and Feldman (1989), Cho and Parlar European Journal of Operational Research 139 (2002) 469–489...

    [...]

  • ...Hundreds of papers and models have been published (McCall (1963), Barlow and Proshan (1965, 1975), Pierskalla and Voelker (1976), Osaki and Nakagawa (1976), Sherif and Smith (1981), Jardine and Buzacott (1985), Valdez-Flores and Feldman (1989), Pham and Wang (1996)) under these two kinds of…...

    [...]

Journal ArticleDOI
TL;DR: In this article, the authors present a short introduction to the field and show some applications for an actuator, a passenger car, and a combustion engine, as well as other types of systems.

1,344 citations

Book ChapterDOI
01 Jan 2003
TL;DR: One main aim of this paper is to show that when addressing the problem of simulating dependent data arises naturally in Monte Carlo approaches to risk management knowledge of copulas and copula based dependence concepts is important, and also the usefulness of copula ideas in this approach torisk management.

1,195 citations