Abstract
A system is subject to a sequence of shocks occurring randomly at timesn= 1, 2, ···; each shock causes a random amount of damage. The system might fail at any point in timen, 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.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
8 articles.
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3. Revisiting discrete time age replacement policy for phase-type lifetime distributions;European Journal of Operational Research;2021-03
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5. Reliability assessment for discrete time shock models via phase‐type distributions;Applied Stochastic Models in Business and Industry;2020-10-08