 Modelling a reliability system governed by discrete phase-type distributionsJuan Eloy Ruiz-Castro, Pérez-Ocón, Rafael and Fernández-Villodre, Gemma Reliability Engineering and System Safety, 2008, vol. 93, issue 11, 1650-1657 Abstract: We present an n-system with one online unit and the others in cold standby. There is a repairman. When the online fails it goes to repair, and instantaneously a standby unit becomes the online one. The operational and repair times follow discrete phase-type distributions. Given that any discrete distribution defined on the positive integers is a discrete phase-type distribution, the system can be considered a general one. A model with unlimited number of units is considered for approximating a system with a great number of units. We show that the process that governs the system is a quasi-birth-and-death process. For this system, performance reliability measures; the up and down periods, and the involved costs are calculated in a matrix and algorithmic form. We show that the discrete case is not a trivial case of the continuous one. The results given in this paper have been implemented computationally with Matlab. Keywords: Phase-type distribution; Stationary distribution; Reliability; Up period; Down period (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:93:y:2008:i:11:p:1650-1657 DOI: 10.1016/j.ress.2008.01.005 Access Statistics for this article Reliability Engineering and System Safety is currently edited by Carlos Guedes Soares More articles in Reliability Engineering and System Safety from Elsevier |
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