{"title":"An Order Statistics Perspective for System Reliability","authors":"Jingzhe Lei, Way Kuo","doi":"10.1002/asmb.2895","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>Structural reliability integrates the design variables over the safety region characterized by a positive limit state function when the reliability of the entire system is of concern. Calculating the structure function can be challenging for high-dimensional systems or intricate system architectures. In order to enhance the efficiency of time-dependent system reliability assessment, we emulate the integral formulation in structural reliability. To elaborate further, we treat each individual unit's lifetime variable as a design variable and subsequently perform calculations involving multiple integrals. Given the ordered nature of unit failure times, we leverage the order statistics distribution to simplify the multiple integrals into a double integral, and then multiply this result by the survival signature to obtain reliability. A two-terminal nine-unit network system configuration is illustrated to assess the performance and effectiveness of the proposed method.</p>\n </div>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 3","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Stochastic Models in Business and Industry","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/asmb.2895","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
Structural reliability integrates the design variables over the safety region characterized by a positive limit state function when the reliability of the entire system is of concern. Calculating the structure function can be challenging for high-dimensional systems or intricate system architectures. In order to enhance the efficiency of time-dependent system reliability assessment, we emulate the integral formulation in structural reliability. To elaborate further, we treat each individual unit's lifetime variable as a design variable and subsequently perform calculations involving multiple integrals. Given the ordered nature of unit failure times, we leverage the order statistics distribution to simplify the multiple integrals into a double integral, and then multiply this result by the survival signature to obtain reliability. A two-terminal nine-unit network system configuration is illustrated to assess the performance and effectiveness of the proposed method.
期刊介绍：
ASMBI - Applied Stochastic Models in Business and Industry (formerly Applied Stochastic Models and Data Analysis) was first published in 1985, publishing contributions in the interface between stochastic modelling, data analysis and their applications in business, finance, insurance, management and production. In 2007 ASMBI became the official journal of the International Society for Business and Industrial Statistics (www.isbis.org). The main objective is to publish papers, both technical and practical, presenting new results which solve real-life problems or have great potential in doing so. Mathematical rigour, innovative stochastic modelling and sound applications are the key ingredients of papers to be published, after a very selective review process.
The journal is very open to new ideas, like Data Science and Big Data stemming from problems in business and industry or uncertainty quantification in engineering, as well as more traditional ones, like reliability, quality control, design of experiments, managerial processes, supply chains and inventories, insurance, econometrics, financial modelling (provided the papers are related to real problems). The journal is interested also in papers addressing the effects of business and industrial decisions on the environment, healthcare, social life. State-of-the art computational methods are very welcome as well, when combined with sound applications and innovative models.
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