Bounds for joint probabilities of multistate systems using preservation of log‐concavity

IF 1.9 4区管理学 Q3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Naval Research Logistics Pub Date : 2023-09-16 DOI:10.1002/nav.22149

Sanjeev Sabnis, Priyanka Majumder, Shyamal Ghosh

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Abstract

Abstract Log‐concavity of multivariate distributions is an important concept in general and has a very special place in the field of Reliability Theory. An attempt has been made in this paper to study preservation results for (i) the discrete version of multivariate log‐concavity for multistate series and multistate parallel systems consisting of independent components, states of both components and systems being represented by elements in a subset of and (ii) the continuous version of multivariate log‐concavity under multistate series and multistate parallel systems made up of independent components and states of both, systems and components, taking values in the set . These results for discrete and continuous versions of log‐concavity have also been extended to systems that are formed using both multistate series and multistate‐parallel systems. Further, the results in (ii) have been used to obtain important and useful bounds on joint probabilities related to times spent by multistate components, multistate series, multistate parallel systems, and the combinations thereof.

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多态系统的联合概率边界，利用对数凹性的保留

多元分布的Log -凹凸性是一个重要的概念，在可靠性理论中占有非常特殊的地位。本文试图研究(i)由独立组件组成的多状态序列和多状态并行系统的多元对数凹性的离散版本，组件和系统的状态由子集中的元素表示;(ii)由独立组件和系统和组件的状态组成的多状态序列和多状态并行系统的多元对数凹性的连续版本。取集合中的值。这些关于对数凹性的离散和连续版本的结果也被推广到由多态序列和多态并行系统组成的系统中。此外，(ii)中的结果已被用于获得与多状态组件、多状态序列、多状态并行系统及其组合所花费时间相关的联合概率的重要和有用的界限。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Naval Research Logistics 管理科学-运筹学与管理科学

CiteScore

4.20

自引率

4.30%

发文量

审稿时长

8 months

期刊介绍： Submissions that are most appropriate for NRL are papers addressing modeling and analysis of problems motivated by real-world applications; major methodological advances in operations research and applied statistics; and expository or survey pieces of lasting value. Areas represented include (but are not limited to) probability, statistics, simulation, optimization, game theory, quality, scheduling, reliability, maintenance, supply chain, decision analysis, and combat models. Special issues devoted to a single topic are published occasionally, and proposals for special issues are welcomed by the Editorial Board.