Tanmay Sahoo, Nil Kamal Hazra, Narayanaswamy Balakrishnan
{"title":"On random weighted coherent systems based on a new structure-based performance measure","authors":"Tanmay Sahoo, Nil Kamal Hazra, Narayanaswamy Balakrishnan","doi":"10.1007/s10479-025-06663-z","DOIUrl":null,"url":null,"abstract":"<div><p>The performance level of a random weighted <i>r</i>-out-of-<i>n</i> system is measured by its total capacity. However, this measure is not meaningful for an arbitrary coherent structure as it does not involve the structure of the system. To overcome this drawback, we introduce here a new notion of performance measure (namely, the structural capacity) and then define three different notions of random weighted coherent systems, namely, Type-I, Type-II and Type-III systems. We then derive explicit formulas for computing the reliabilities of these systems. We further give a signature-based reliability representation for these systems. Further, we derive the Birnbaum marginal and joint reliability importance measures for the components of these systems and subsequently provide an algorithm for computing the same. Then, we study several ordering results based on these importance measures. For the Type-III random weighted coherent system, we introduce a new structure-based weighted importance measure and provide an algorithm for its evaluation. The developed results are illustrated through several numerical examples. Finally, we carry out the reliability estimation for a random weighted coherent system using two different simulated data sets.</p></div>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":"350 3","pages":"1169 - 1206"},"PeriodicalIF":4.5000,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Operations Research","FirstCategoryId":"91","ListUrlMain":"https://link.springer.com/article/10.1007/s10479-025-06663-z","RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
The performance level of a random weighted r-out-of-n system is measured by its total capacity. However, this measure is not meaningful for an arbitrary coherent structure as it does not involve the structure of the system. To overcome this drawback, we introduce here a new notion of performance measure (namely, the structural capacity) and then define three different notions of random weighted coherent systems, namely, Type-I, Type-II and Type-III systems. We then derive explicit formulas for computing the reliabilities of these systems. We further give a signature-based reliability representation for these systems. Further, we derive the Birnbaum marginal and joint reliability importance measures for the components of these systems and subsequently provide an algorithm for computing the same. Then, we study several ordering results based on these importance measures. For the Type-III random weighted coherent system, we introduce a new structure-based weighted importance measure and provide an algorithm for its evaluation. The developed results are illustrated through several numerical examples. Finally, we carry out the reliability estimation for a random weighted coherent system using two different simulated data sets.
期刊介绍:
The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications.
In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.