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Optimal replacement in a shock model: discrete time

Published online by Cambridge University Press:  14 July 2016

Terje Aven  and
Simen Gaarder
Terje Aven*
Affiliation:
Rogaland College
Simen Gaarder
Affiliation:
University of Oslo
*
∗Postal address: Rogaland College, Box 2540, Ullandhaug, 4001 Stavanger, Norway.
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Abstract

A system is subject to a sequence of shocks occurring randomly at times n = 1, 2, ···; each shock causes a random amount of damage. The system might fail at any point in time n, and the probability of a failure depends on the history of the system. Upon failure the system is replaced by a new and identical system and a cost is incurred. If the system is replaced before failure a smaller cost is incurred. We study the problem of specifying a replacement rule which minimizes the long-run (expected) average cost per unit time. A special case, in which the system fails when the total damage first exceeds a fixed threshold, is analysed in detail.

Keywords

REPLACEMENTSTOPPING TIMEAVERAGE COST
Type
Short Communications
Information
Journal of Applied Probability , Volume 24 , Issue 1 , March 1987 , pp. 281 - 287
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

∗∗

Present address: Gjensidige Insurance Co., Box 6738, St. Olavs pl., 0130 Oslo 1, Norway.

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