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Optimum replacement of a system subject to shocks

Published online by Cambridge University Press:  14 July 2016

Mohamed Abdel-Hameed
Mohamed Abdel-Hameed*
Affiliation:
University of North Carolina
*
∗ Present address: Department of Mathematics, Kuwait University, P.O. Box 5969, Kuwait. Research supported by Air Force Office of Scientific Research Grant AFOSR-80–0245.
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Abstract

A system is subject to shocks. Each shock weakens the system and makes it more expensive to run. It is desirable to determine a replacement time for the system. Boland and Proschan [4] consider periodic replacement of the system and give sufficient conditions for the existence of an optimal finite period, assuming that the shock process is a non-homogeneous Poisson process and the cost structure does not depend on time. Block et al. [3] establish similar results assuming that cost structure is time dependent, still requiring that the shock process is a non-homogeneous Poisson process. We show via a sample path argument that the results of [3] and [4] hold for any counting process whose jump size is of one unit magnitude.

Keywords

PERIODIC REPLACEMENTNON-HOMOGENEOUS PURE BIRTH PROCESSRENEWAL PROCESSRENEWAL FUNCTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 23 , Issue 1 , March 1986 , pp. 107 - 114
Copyright
Copyright © Applied Probability Trust 1986 

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References

[1] Abdel-Hameed, M. S. (1984) Life distribution properties of devices subject to a Lévy wear process. Math. Operat. Res. 9, 606–614.CrossRefGoogle Scholar
[2] Abdel-Hameed, ?. S. and Proschan, F. (1975) Shock models with underlying birth process. J. Appl. Prob. 12, 18–28.Google Scholar
[3] Block, H. W., Borges, W. S. and Savits, T. H. (1983) A general minimal repair maintenance model. University of Pittsburgh Technical Report No. 83-17.Google Scholar
[4] Boland, P. J. and Proschan, F. (1983) Optimum replacement of a system subject to shocks. Operat. Res. 31, 697–704.Google Scholar