Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-06-17T02:18:31.788Z Has data issue: false hasContentIssue false
  • English
  • Français

On the optimality of stationary replacement strategies

Published online by Cambridge University Press:  14 July 2016

Bo Bergman
Bo Bergman*
Affiliation:
Saab-Scania AB, Linköping and University of Lund
*
∗Postal address: Saab-Scania Aerospace Division, S–58 188 Linköping, Sweden.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper it is shown that for a large class of replacement problems the class of stationary replacement strategies is complete, i.e. in order to minimize the average long run cost per unit time it suffices to consider replacement rules which are equal for each new unit irrespectively of what has been observed from earlier units. The main result is based on a version of the law of large numbers for martingale differences proved in the appendix.

Keywords

REPLACEMENT THEORYRENEWAL THEORYSTATIONARY DECISION STRATEGIESOPTIMALITYMARTINGALE DIFFERENCESLAW OF LARGE NUMBERS
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 1 , March 1980 , pp. 178 - 186
Copyright
Copyright © Applied Probability Trust 1980 

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
Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing, Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
Berg, M. (1976) A proof of optimality for age replacement policies. J. Appl. Prob. 13, 751–759.Google Scholar
Bergman, B. (1978) Optimal replacement under a general failure model. Adv. Appl. Prob. 10, 431–451.Google Scholar
Bergman, B. (1979) On age replacement and the total time on test concept. Scand. J. Statist. 6, 161–168.Google Scholar
Chung, K. L. (1974) A course in Probability Theory, 2nd edn. Academic Press, New York.Google Scholar
Feldman, R. M. (1976) Optimal replacement with semi-Markov shock models. J. Appl. Prob. 13, 108–117.Google Scholar
Feller, W. (1971) An Introduction to Probability Theory and its Applications, Vol. II, 2nd edn. Wiley, New York.Google Scholar
Kao, E. P. E. (1973) Optimal replacement rules when changes of states are semi-Markovian. Operat. Res. 21, 1231–1249.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.Google Scholar
Ross, S. M. (1971) On the non-existence of e -optimal randomized stationary policies in average cost Markov decision models. Ann. Math. Statist. 42, 1767–1768.Google Scholar
Taylor, H. M. (1975) Optimal replacement under additive damage and other failure models. Naval Res. Log. Quart. 22, 1–18.Google Scholar