New failure and minimal repair processes for repairable systems in a random environment
- 주제(키워드) cumulative shock model , extreme shock model , information-based minimal repair , nonhomogeneous poisson process , random environment , statistical minimal repair
- 주제(기타) Operations Research & Management Science; Mathematics, Interdisciplinary Applications; Statistics & Probability
- 설명문(일반) [Cha, Ji Hwan] Ewha Womans Univ, Dept Stat, Seoul 120750, South Korea; [Finkelstein, Maxim] Univ Free State, Dept Math Stat, ZA-9300 Bloemfontein, South Africa; [Finkelstein, Maxim] ITMO Univ, Adapt & Nonlinear Control Syst Lab, St Petersburg 19710, Russia
- 등재 SCIE, SCOPUS
- 발행기관 WILEY
- 발행년도 2019
- URI http://www.dcollection.net/handler/ewha/000000160121
- 본문언어 영어
- Published As http://dx.doi.org/10.1002/asmb.2331
초록/요약
Most often, minimal repair is defined as a replacement of a failed item by an operable item that has the same distribution of the remaining lifetime as the failed one just prior a failure. This is the so-called statistical minimal repair extensively explored in the literature. Another well-known type of minimal repair takes into account the state of a system prior to a failure (the information-based minimal repair). In this paper, we suggest the new type of minimal repair to be called conditional statistical minimal repair. Our approach goes further and deals with the corresponding minimal repair processes for systems operating in a random environment. Moreover, we also consider heterogeneous populations of items, which makes the model more realistic. Both of these aspects that affect the failure mechanism of items are studied. Environment is modeled by the nonhomogeneous Poisson shock process. Two models for the failure mechanism defined by the extreme shock model and the cumulative shock model, respectively, are considered. Some examples illustrating our findings are presented.
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