Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T17:19:35.377Z Has data issue: false hasContentIssue false
  • English
  • Français

Comparison of two replacement policies

Published online by Cambridge University Press:  14 July 2016

Antonín Lešanovský
Antonín Lešanovský*
Affiliation:
Mathematical Institute, Prague
*
∗Postal address: Mathematical Institute of the Czechoslovak Academy of Siences, Žitná 25, 115 67 Prague 1, Czechoslovakia.
Get access Rights & Permissions [Opens in a new window]

Abstract

Two models of a system with a single activated unit which can be in a finite number of states are considered. The unit is subject to Markovian deterioration, and it is possible to replace it before its failure. Inspections of the system are carried out at discrete time instants. The only difference between the two models is when the replacements take effect — immediately at the instant when the corresponding decision is made, or with the next inspection. The paper shows that this difference is much more essential than one might expect, and proves a relation between the optimal replacement strategies in the models concerned.

Keywords

ONE-UNIT SYSTEMMARKOVIAN DETERIORATIONAVERAGE COST CRITERION
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986 , pp. 759 - 769
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

[1] Derman, C. (1970) Finite State Markovian Decision Processes. Mathematics in Science and Engineering 67, Academic Press, New York.Google Scholar
[2] Derman, C. (1966) Denumerable state markovian decision processes — average cost criterion. Ann. Math. Statist. 37, 1545–1553.Google Scholar
[3] Kasumu, R. A. and Lešanovský, A. (1983) On optimal replacement policy. Apl. Mat. 28, 317–329.Google Scholar
[4] Kawai, H. (1983) An optimal ordering and replacement policy of a markovian deterioration system under incomplete observation — Part II. J. Operat. Res. Soc. Japan 26, 293–308.Google Scholar
[5] Kolesar, P. (1966) Minimum cost replacement under markovian deterioration. Management Sci. 12, 694–706.Google Scholar
[6] Lešanovský, A. (1986) A remark on optimality of control limit rules. Management Sci. Google Scholar
[7] Mine, H. and Kawai, H. (1977) Optimal ordering and replacement for a 1-unit system. IEEE Trans. Reliability 26, 273–276.CrossRefGoogle Scholar
[8] Rosenfield, D. B. (1974) Deteriorating Markov processes under uncertainty. Technical report No. 162, Department of Operations Research and Department of Statistics, Stanford University.Google Scholar