Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-23T21:36:26.906Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal replacement with semi-Markov shock models

Published online by Cambridge University Press:  14 July 2016

Richard M. Feldman
Richard M. Feldman*
Affiliation:
Northwestern Universitycor1corresp
*
Get access Rights & Permissions [Opens in a new window]

Abstract

Consider a system that is subject to a sequence of randomly occurring shocks; each shock causes some damage of random magnitude to the system. Any of the shocks might cause the system to fail, and the probability of such a failure is a function of the sum of the magnitudes of damage caused from all previous shocks.

The purpose of this paper is to derive the optimal replacement rule for such a system whose cumulative damage process is a semi-Markov process. This allows for both the time between shocks and the damage due to the next shock to be dependent on the present cumulative damage level.

Only policies within the class of control-limit policies will be considered; namely, policies with which no action is taken if the damage is below a fixed level, and a replacement is made if the damage is above that.

An example will be given illustrating the use of the optimal replacement rule.

Keywords

OPTIMAL REPLACEMENTSEMI-MARKOV PROCESSESMARKOV RENEWAL THEORY
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 1 , March 1976 , pp. 108 - 117
Copyright
Copyright © Applied Probability Trust 1976 

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.)

Footnotes

Research supported by the Air Force Office of Scientific Research through their Grant No. AFOSR–74–2733.

References

Çinlar, E. (1969) On semi-Markov processes on arbitrary spaces. Proc. Camb. Phil. Soc. 66, 381–392.Google Scholar
Çinlar, E. (1975) Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, N. J.Google Scholar
Kao, E. P. C. (1973) Optimal replacement rules when changes of state are semi-Markovian. Operations Res. 21, 1231–1249.Google Scholar
Ross, S.M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar
Taylor, H. M. (1975) Optimal replacement under additive damage and other failure models. Naval Res. Logist. Quart. 22, 1–18.CrossRefGoogle Scholar