Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-25T12:32:03.648Z Has data issue: false hasContentIssue false
  • English
  • Français

A repair replacement model

Published online by Cambridge University Press:  01 July 2016

Lam Yeh
Lam Yeh*
Affiliation:
The Chinese University of Hong Kong
*
∗Postal address: Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we study a similar replacement model in which the successive survival times of the system form a process with non-increasing means, whereas the consecutive repair times after failure constitute a process with non-decreasing means. The system is replaced at the time of the Nth failure since the installation or last replacement. Based on the long-run average cost per unit time, we determine the optimal replacement policy N∗ and the maximum of the long-run average reward explicitly. Under additional conditions, the policy N∗ is even optimal among all replacement policies.

Keywords

IFRNBUERENEWAL THEORY
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 22 , Issue 2 , June 1990 , pp. 494 - 497
Copyright
Copyright © Applied Probability Trust 1990 

References

Ascher, H. and Feingold, H. (1984) Repairable Systems Reliability. Marcel Dekker, New York.Google Scholar
Barlow, R. E. and Proschan, F. (1965) Mathematical Theory of Reliability. Wiley, New York.Google Scholar
Downton, F. (1971) Stochastic models for successive failures. Proc. 38th Session Internat. Statist. Inst. 44 (1), 667–694.Google Scholar
Yeh, Lam (1988a) A note on the optimal replacement problem. Adv. Appl. Prob. 20, 479–482.CrossRefGoogle Scholar
Yeh, Lam (1988b) Geometric process and replacement problem. Acta Math. Appl. Sinica 4, 366–377.Google Scholar
Morimura, H. (1970) On some preventive maintenance policies for IFR. J. Operat. Res. Soc. Japan 12, 94–124.Google Scholar
Nakagawa, T. (1984) Discrete Replacement Models. Stochastic Models in Reliability. Lecture Notes in Economics and Mathematical Systems 235, Springer-Verlag, Berlin.Google Scholar
Stadje, W. and Zuckerman, D. (1990) Optimal strategies for some repair replacement models. Adv. Appl. Prob. 22 (3).CrossRefGoogle Scholar
Thompson, W. A. (1981) On the foundations of reliability. Technometrics 23, 1–13.CrossRefGoogle Scholar