Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-10T07:01:44.169Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the optimal replacement problem

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 note, we study a new repair replacement model for a deteriorating system, in which the successive survival times of the system form a geometric process and are stochastically non-increasing, whereas the consecutive repair times after failure also constitute a geometric process but are stochastically non-decreasing. Two kinds of replacement policy are considered, one based on the working age of the system and the other one determined by the number of failures. The explicit expressions of the long-run average costs per unit time under these two kinds of policy are calculated.

Keywords

REPLACEMENT PROBLEMSTOCHASTIC MONOTONICITYRENEWAL PROCESSES
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 20 , Issue 2 , June 1988 , pp. 479 - 482
Copyright
Copyright © Applied Probability Trust 1988 

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
Yeh, Lam (1987) Geometric Processes and Replacement Problem. Technical Report 42, Department of Statistics, The Chinese University of Hong Kong.Google Scholar
Morimura, H. (1970) On some preventive maintenance policies for IFR. J. Operat. Res. Soc. Japan. 12, 94–124.Google Scholar
Ross, S. M. (1970). Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar
Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar