2018
DOI: 10.1002/nav.21820
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Stochastic comparisons of replacement policies in coherent systems under minimal repair

Abstract: In this paper, we study stochastic comparisons of the coherent systems obtained under different repair policies. We consider minimal repairs of the components, that is, a failed component is replaced by another component which is similar (ie, it has the same distribution) to the replaced one and with the same age. Under these assumptions, we study how to determine the best replacement policies. Two general methods are proposed, one for systems with identically distributed components and another one for systems… Show more

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Cited by 19 publications
(25 citation statements)
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“…components. Our findings strengthen and generalize some corresponding ones in Shaked and Shanthikumar () and solve the open problems posed in Chahkandi et al () and Arriaza et al ().…”
Section: Discussionsupporting
confidence: 92%
See 4 more Smart Citations
“…components. Our findings strengthen and generalize some corresponding ones in Shaked and Shanthikumar () and solve the open problems posed in Chahkandi et al () and Arriaza et al ().…”
Section: Discussionsupporting
confidence: 92%
“…We prove that both the reversed hazard function of T p ( k ) and the hazard rate function of T s ( k ) are Schur‐convex in k , which means that the optimal allocation policy can be respectively reached by putting all minimal repairs in one component for the parallel system in the sense of the reversed hazard rate ordering, and allocating the minimal repairs in balance as much as possible for the series system in the sense of the hazard rate ordering. These results not only strengthen the counterparts of Shaked and Shanthikumar () in the usual stochastic order to the reversed hazard rate order (for parallel system) and hazard rate order (for series system), respectively, but also solve the open problems proposed by Arriaza et al () and Chahkandi et al (). With the help of some numerical examples, we show that the hazard (reversed hazard) rate order does not hold for parallel (series) systems with more than three components when an allocation vector is more heterogeneous than another one.…”
Section: Introductionsupporting
confidence: 81%
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