Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-26T12:58:00.606Z Has data issue: false hasContentIssue false
  • English
  • Français

A bivariate optimal replacement policy for a repairable system

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Yuan Lin Zhang
Yuan Lin Zhang*
Affiliation:
Southeast University, Nanjing
*
∗Postal address: Department of Mathematics and Mechanics, Southeast University, Nanjing 210018, People's Republic of China.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, a repairable system consisting of one unit and a single repairman is studied. Assume that the system after repair is not as good as new. Under this assumption, a bivariate replacement policy (T, N), where T is the working age and N is the number of failures of the system is studied. The problem is to determine the optimal replacement policy (T, N)∗such that the long-run average cost per unit time is minimized. The explicit expression of the long-run average cost per unit time is derived, and the corresponding optimal replacement policy can be determined analytically or numerically. Finally, under some conditions, we show that the policy (T, N)∗ is better than policies N∗ or T∗.

Keywords

GEOMETRIC PROCESSRENEWAL PROCESSRENEWAL CYCLERENEWAL REWARD THEOREMCONVOLUTION

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 31 , Issue 4 , December 1994 , pp. 1123 - 1127
Copyright
Copyright © Applied Probability Trust 1994 

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. (1965) Mathematical Theory of Reliability. Wiley, New York.Google Scholar
Yeh, Lam (1988a) A note on the optimal replacement problem. Adv. Appl. Prob. 20, 479–482.CrossRefGoogle Scholar
Yeh, Lam (1988b) Geometric processes and replacement problem. Acta. Math. Appl. Sinica 4, 366–377.Google Scholar
Yeh, Lam (1990) A repair replacement model. Adv. Appl. Prob. 22, 494–497.CrossRefGoogle Scholar
Lotka, A. J. (1939) A contribution to the theory of self-renewing aggregates with special reference to industrial replacement. Ann. Math. Statist. 10, 1–25.CrossRefGoogle Scholar
Park, K. S. (1979) Optimal number of minimal repairs before replacement. IEEE Trans. Reliability 28, 137–140.CrossRefGoogle Scholar
Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar
Stadje, W. and Zuckerman, D. (1990) Optimal strategies for some repair replacement models. Adv. Appl. Prob. 22, 641–656.CrossRefGoogle Scholar