Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T05:18:49.903Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

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

[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