{"title":"使用霍克斯流程对单机系统进行维护计划评估和策略优化","authors":"Lirong Cui, Fengming Kang, Jingyuan Shen","doi":"10.1080/16843703.2022.2093817","DOIUrl":null,"url":null,"abstract":"ABSTRACT Maintenance planning and optimizations are very important issues in both theory and practice. In this paper, Hawkes processes, a tool for description of self-excited failure effects, are used to model the failure processes of single-unit systems under the assumption of neglected repair times. For such degraded single-unit systems, some maintenance planning estimations such as the distribution, mean and variance of failures or repairs by time , reliability, mean cost of maintenance, mean and variance of system lifetime are presented under the maximal entropy assumption on repair effects. Meanwhile, two optimization problems are developed by considering the lifetime mean of the single-unit system and total maintenance cost as objective functions and constraints alternatively. We have proved that both optimization problems can reduce to two simplified optimal cases, respectively, and their optimal policies are increasing stepwise sequences of increasing rates of failure rates, which greatly reduce the scope of optimal solutions. The relationships between the estimations and the optimizations are discussed. Furthermore, the detailed optimal maintenance policies for a special case are given as well including an algorithm.","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"20 1","pages":"211 - 235"},"PeriodicalIF":2.3000,"publicationDate":"2022-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Maintenance planning estimations and policies optimization for single-unit systems using Hawkes processes\",\"authors\":\"Lirong Cui, Fengming Kang, Jingyuan Shen\",\"doi\":\"10.1080/16843703.2022.2093817\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"ABSTRACT Maintenance planning and optimizations are very important issues in both theory and practice. In this paper, Hawkes processes, a tool for description of self-excited failure effects, are used to model the failure processes of single-unit systems under the assumption of neglected repair times. For such degraded single-unit systems, some maintenance planning estimations such as the distribution, mean and variance of failures or repairs by time , reliability, mean cost of maintenance, mean and variance of system lifetime are presented under the maximal entropy assumption on repair effects. Meanwhile, two optimization problems are developed by considering the lifetime mean of the single-unit system and total maintenance cost as objective functions and constraints alternatively. We have proved that both optimization problems can reduce to two simplified optimal cases, respectively, and their optimal policies are increasing stepwise sequences of increasing rates of failure rates, which greatly reduce the scope of optimal solutions. The relationships between the estimations and the optimizations are discussed. Furthermore, the detailed optimal maintenance policies for a special case are given as well including an algorithm.\",\"PeriodicalId\":49133,\"journal\":{\"name\":\"Quality Technology and Quantitative Management\",\"volume\":\"20 1\",\"pages\":\"211 - 235\"},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2022-08-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quality Technology and Quantitative Management\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1080/16843703.2022.2093817\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, INDUSTRIAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quality Technology and Quantitative Management","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1080/16843703.2022.2093817","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, INDUSTRIAL","Score":null,"Total":0}
Maintenance planning estimations and policies optimization for single-unit systems using Hawkes processes
ABSTRACT Maintenance planning and optimizations are very important issues in both theory and practice. In this paper, Hawkes processes, a tool for description of self-excited failure effects, are used to model the failure processes of single-unit systems under the assumption of neglected repair times. For such degraded single-unit systems, some maintenance planning estimations such as the distribution, mean and variance of failures or repairs by time , reliability, mean cost of maintenance, mean and variance of system lifetime are presented under the maximal entropy assumption on repair effects. Meanwhile, two optimization problems are developed by considering the lifetime mean of the single-unit system and total maintenance cost as objective functions and constraints alternatively. We have proved that both optimization problems can reduce to two simplified optimal cases, respectively, and their optimal policies are increasing stepwise sequences of increasing rates of failure rates, which greatly reduce the scope of optimal solutions. The relationships between the estimations and the optimizations are discussed. Furthermore, the detailed optimal maintenance policies for a special case are given as well including an algorithm.
期刊介绍:
Quality Technology and Quantitative Management is an international refereed journal publishing original work in quality, reliability, queuing service systems, applied statistics (including methodology, data analysis, simulation), and their applications in business and industrial management. The journal publishes both theoretical and applied research articles using statistical methods or presenting new results, which solve or have the potential to solve real-world management problems.