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Some results for repairable systems with general repair

Published online by Cambridge University Press:  14 July 2016

Masaaki Kijima
Masaaki Kijima*
Affiliation:
Tokyo Institute of Technology
*
∗Postal address: Department of Information Sciences, Tokyo Institute of Technology, Meguro-ku, Tokyo 152, Japan.
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Abstract

In this paper, we develop general repair models for a repairable system by using the idea of the virtual age process of the system. If the system has the virtual age Vn –1 = y immediately after the (n – l)th repair, the nth failure-time Xn is assumed to have the survival function where is the survival function of the failure-time of a new system. A general repair is represented as a sequence of random variables An taking a value between 0 and 1, where An denotes the degree of the nth repair. For the extremal values 0 and 1, An = 1 means a minimal repair and An= 0 a perfect repair. Two models are constructed depending on how the repair affects the virtual age process: Vn = Vn– 1+ AnXn as Model 1 and Vn = An(Vn– 1 + Xn) as Model II. Various monotonicity properties of the process with respect to stochastic orderings of general repairs are obtained. Using a result, an upper bound for E[Sn] when a general repair is used is derived.

Keywords

MINIMAL REPAIRSTOCHASTIC ORDERING
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 1 , March 1989 , pp. 89 - 102
Copyright
Copyright © Applied Probability Trust 1989 

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