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An identity for Markovian replacement processes

Published online by Cambridge University Press:  14 July 2016

Petr Mandl
Petr Mandl*
Affiliation:
Australian National University
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Summary

A Markovian process with rewards is considered. The interference into its development consists in instantaneous changes of state called replacements. It is shown that, for any replacement policy not depending on the future, the expected reward is a linear function of the expected replacement numbers. The application of this result is illustrated by examples.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 2 , August 1969 , pp. 348 - 354
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

[1] Derman, C. (1963) Optimal replacement and maintenance under Markovian deterioration with probability bounds on failure. Management Sci. 9, 478–481.Google Scholar
[2] Howard, R. A. (1960) Dynamic Programming and Markov Processes. MIT Press and John Wiley, New York and London.Google Scholar