Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-28T19:20:19.110Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal stopping in a semi-Markov shock model

Published online by Cambridge University Press:  14 July 2016

Dror Zuckerman
Dror Zuckerman*
Affiliation:
The Hebrew University of Jerusalem
Get access Rights & Permissions [Opens in a new window]

Abstract

We examine a failure model for a system existing in a random environment. The system accumulates damage through a shock process and the failure time depends on the accumulated damage in the system. The cumulative damage process is assumed to be a semi-Markov process. Upon failure the system must be replaced by a new identical one and a failure cost is incurred. If the system is replaced before failure, a smaller cost is incurred. We allow a controller to replace the system at any stopping time before failure time. We consider the problem of specifying a replacement rule which minimizes the total long-run average cost per unit time.

Keywords

REPLACEMENT POLICYSEMI-MARKOV PROCESSSTOPPING TIMECONTROL LIMIT POLICYINFINITESIMAL OPERATORHAZARD RATE
Type
Short Communications
Information
Journal of Applied Probability , Volume 15 , Issue 3 , September 1978 , pp. 629 - 634
Copyright
Copyright © Applied Probability Trust 1978 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Barlow, R. E. and Proschan, F. (1965) Mathematical Theory of Reliability. Wiley, New York.Google Scholar
[2] Dynkin, E. B. (1965) Markov Processes 1. Academic Press, New York.Google Scholar
[3] Feldman, R. M. (1976) Optimal replacement with semi-Markov shock models. J. Appl. Prob. 13, 108–117.Google Scholar
[4] Kao, E. P. C. (1973) Optimal replacement rules when changes of state are semi-Markovian. Opns Res. 21, 1231–1249.CrossRefGoogle Scholar
[5] Taylor, H. M. (1975) Optimal replacement under additive damage and other failure models. Naval Res. Logist. Quart. 22, 1–18.Google Scholar