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Some results on Markovian replacement processes

Published online by Cambridge University Press:  14 July 2016

Petr Mandl
Petr Mandl*
Affiliation:
University of Manchester
*
* Permanent address: Czechoslovak Academy of Sciences, Institute of Information Theory and Automation, Prague.
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Summary

A replacement of type (jk) in a Markov process with rewards means an instantaneous shift of the trajectory from state j into state k. A formula is obtained for the characteristic function of the total reward from the process under an arbitrary non-anticipative replacement policy. From the formula results are deduced concerning Markov policies, optimal policies and policies minimizing the variance of the reward.

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 2 , June 1971 , pp. 357 - 365
Copyright
Copyright © Applied Probability Trust 1971 

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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.CrossRefGoogle Scholar
[2] Howard, R. A. (1960) Dynamic Programming and Markov Processes. M.I.T. Press and John Wiley, New York and London.Google Scholar
[3] Mandl, P. (1969) An identity for Markovian replacement processes. J. Appl. Prob. 6, 348–354.CrossRefGoogle Scholar