Hostname: page-component-7bb8b95d7b-lvwk9 Total loading time: 0 Render date: 2024-09-12T10:07:13.404Z Has data issue: false hasContentIssue false
  • English
  • Français

Semi-Markov shock models with additive damage

Published online by Cambridge University Press:  01 July 2016

M. J. M. Posner  and
D. Zuckerman
M. J. M. Posner*
Affiliation:
University of Toronto
D. Zuckerman*
Affiliation:
Hebrew University of Jerusalem
*
∗Postal address: Department of Industrial Engineering, University of Toronto, Toronto, Ont., M5S 1A4, Canada.
∗∗Present address: Faculty of Commerce and Business Administration, The University of British Columbia, 2053 Main Mall, Vancouver BC, V6T 1Y8, Canada.
Get access Rights & Permissions [Opens in a new window]

Abstract

We examine a replacement model for a semi-Markov shock model with additive damage. Sufficient conditions are given for the optimality of control limit policies. The paper generalizes and unifies previous research in the area.

In addition, we investigate in detail the practical modelling and computational aspects of the replacement problem using a semi-Markov modelling structure.

Keywords

OPTIMAL REPLACEMENTCONTROL LIMIT POLICYMARKOV RENEWAL PROCESSOPTIMAL STOPPINGINFINITESIMAL KILLING RATELEXICOGRAPHIC ORDER
Type
Research Article
Information
Advances in Applied Probability , Volume 18 , Issue 3 , September 1986 , pp. 772 - 790
Copyright
Copyright © Applied Probability Trust 1986 

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

Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
Feldman, R. M. (1976) Optimal replacement with semi-Markov shock models. J. Appl. Prob. 13, 108–117.CrossRefGoogle Scholar
Feldman, R. M. (1977) Optimal replacement with semi-Markov shock models using discounted cost. Math. Operat. Res. 2, 78–90.CrossRefGoogle Scholar
Gottlieb, G. (1982) Optimal replacement for shock models with general failure rate. Operat. Res. 30, 82–92.CrossRefGoogle Scholar
Howard, R. A. (1971) Dynamic Probabilistic Systems, Vol. II: Semi-Markov and Decision Processes. Wiley, New York.Google Scholar
Pierskalla, W. P. and Voelker, J. A. (1976) A survey of maintenance models: the control and surveillance of deteriorating systems. Naval Res. Log. Quart. 23, 353–388.CrossRefGoogle Scholar
Posner, M. J. M. and Zuckerman, D. (1984) A replacement model for an additive damage model with restoration. Operat. Res. Letters. 3, 141–148.CrossRefGoogle Scholar
Taylor, H. M. (1968) Optimal stopping in a Markov process. Ann. Math. Statist. 39, 1333–1344.CrossRefGoogle Scholar
Taylor, H. M. (1975) Optimal replacement under additive damage and other failure models. Naval Res. Log. Quart. 22, 1–18.CrossRefGoogle Scholar
Zuckerman, D. (1978a) Optimal replacement policy for the case where the damage process is a one-sided Lévy process. Stoch. Proc. Appl. 7, 141–151.CrossRefGoogle Scholar
Zuckerman, D. (1978b) Optimal stopping in a semi-Markov shock model. J. Appl. Prob. 15, 629–634.Google Scholar