Optimal number of minimal repairs with cumulative repair cost limit for a two-unit system with failure rate interactions. Issue 2 (25th January 2016)

• Record Type: Journal Article
• Authors: Lai, Min-Tsai; Yan, Huey
• Is Part Of: International journal of systems science. Volume 47:Issue 2(2016)
• Page Start: 466
• Page End: 473
• Publication Date: 2016-01-25
• Subjects: two-unit system -- failure rate interaction -- cumulative repair cost limit -- discrete replacement model; System analysis -- Periodicals; 003.3
• DOI: 10.1080/00207721.2014.886749
• Languages: English
• ISSNs: 0020-7721

Abstract

Abstract : A discrete replacement model is presented that includes a cumulative repair cost limit for a two-unit system with failure rate interactions between the units. We assume a failure in unit 1 causes the failure rate in unit 2 to increase, whereas a failure in unit 2 causes a failure in unit 1, resulting in a total system failure. If unit 1 fails and the cumulative repair cost till to this failure is less than a limit L, then unit 1 is repaired. If there is a failure in unit 1 and the cumulative repair cost exceeds L or the number of failures equals n, the entire system is preventively replaced. The system is also replaced at a total failure, and such replacement cost is higher than the preventive replacement cost. The long-term expected cost per unit time is derived using the expected costs as the optimality criterion. The minimum-cost policy is derived, and existence and uniqueness are proved.