{"title":"An algorithm to construct coherent systems using signatures","authors":"T. V. Rao, Sameen Naqvi","doi":"10.1017/jpr.2024.60","DOIUrl":null,"url":null,"abstract":"<p>The system signature is a useful tool for studying coherent systems. For a given coherent system, various methods have been proposed in the literature to compute its signature. However, when any system signature is given, the literature does not address how to construct the corresponding coherent system(s). In this article we propose an algorithm to address this research gap. This algorithm enables the validation of whether a provided probability vector qualifies as a signature. If it does, the algorithm proceeds to generate the corresponding coherent system(s). To illustrate the applicability of this algorithm, we consider all three and four-dimensional probability vectors, verify if they are signatures, and finally obtain 5 and 20 coherent systems, respectively, which coincides with the literature (Shaked and Suarez-Llorens 2003).</p>","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Probability","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/jpr.2024.60","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
The system signature is a useful tool for studying coherent systems. For a given coherent system, various methods have been proposed in the literature to compute its signature. However, when any system signature is given, the literature does not address how to construct the corresponding coherent system(s). In this article we propose an algorithm to address this research gap. This algorithm enables the validation of whether a provided probability vector qualifies as a signature. If it does, the algorithm proceeds to generate the corresponding coherent system(s). To illustrate the applicability of this algorithm, we consider all three and four-dimensional probability vectors, verify if they are signatures, and finally obtain 5 and 20 coherent systems, respectively, which coincides with the literature (Shaked and Suarez-Llorens 2003).
期刊介绍:
Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used.
A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.