{"title":"On the combined imperfect repair process","authors":"Ji Hwan Cha, Maxim Finkelstein","doi":"10.1017/s0269964823000177","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, a new point process is introduced. It combines the nonhomogeneous Poisson process with the generalized Polya process (GPP) studied in recent literature. In reliability interpretation, each event (failure) from this process is minimally repaired with a given probability and GPP-repaired with the complementary probability. Characterization of the new process via the corresponding bivariate point process is presented. The mean numbers of events for marginal processes are obtained via the corresponding rates, which are used for considering an optimal replacement problem as an application.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"189 1","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probability in the Engineering and Informational Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/s0269964823000177","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENGINEERING, INDUSTRIAL","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract In this paper, a new point process is introduced. It combines the nonhomogeneous Poisson process with the generalized Polya process (GPP) studied in recent literature. In reliability interpretation, each event (failure) from this process is minimally repaired with a given probability and GPP-repaired with the complementary probability. Characterization of the new process via the corresponding bivariate point process is presented. The mean numbers of events for marginal processes are obtained via the corresponding rates, which are used for considering an optimal replacement problem as an application.
期刊介绍：
The primary focus of the journal is on stochastic modelling in the physical and engineering sciences, with particular emphasis on queueing theory, reliability theory, inventory theory, simulation, mathematical finance and probabilistic networks and graphs. Papers on analytic properties and related disciplines are also considered, as well as more general papers on applied and computational probability, if appropriate. Readers include academics working in statistics, operations research, computer science, engineering, management science and physical sciences as well as industrial practitioners engaged in telecommunications, computer science, financial engineering, operations research and management science.
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