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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.
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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 

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