Optimal replacement in a shock model: discrete time
- 1 March 1987
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 24 (1) , 281-287
- https://doi.org/10.2307/3214082
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
This publication has 11 references indexed in Scilit:
- Optimal replacement times — a general set-upJournal of Applied Probability, 1986
- Point Processes and QueuesPublished by Springer Nature ,1981
- A General Failure Model: Optimal Replacement with State Dependent Replacement and Failure CostsMathematics of Operations Research, 1980
- Optimal replacement rule-discounted cost criterionRairo-Operations Research, 1979
- Optimal replacement policy for the case where the damage process is a one-sided Lévy processStochastic Processes and their Applications, 1978
- Optimal stopping in a semi-Markov shock modelJournal of Applied Probability, 1978
- Optimal replacement of damaged devicesJournal of Applied Probability, 1978
- Optimal replacement under a general failure modelAdvances in Applied Probability, 1978
- Optimal replacement with semi-Markov shock modelsJournal of Applied Probability, 1976
- Optimal replacement under additive damage and other failure modelsNaval Research Logistics Quarterly, 1975