Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-24T17:25:31.687Z Has data issue: false hasContentIssue false
  • English
  • Français

A non-Markov model for the optimum replacement of self-repairing systems subject to shocks

Published online by Cambridge University Press:  14 July 2016

A. Rangan  and
R. Esther Grace
A. Rangan*
Affiliation:
IIT Madras
R. Esther Grace*
Affiliation:
IIT Madras
*
∗Postal address: Department of Mathematics, Indian Institute of Technology, Madras 600 036, India.
∗Postal address: Department of Mathematics, Indian Institute of Technology, Madras 600 036, India.
Get access Rights & Permissions [Opens in a new window]

Abstract

A system is subject to shocks; each shock at time t increases the cumulative damage λ (t) by a constant amount, while the system is subject to repair in between the shocks which brings down λ (t) at a constant rate. The shock arrival process is an inhomogeneous Poisson process with intensity function λ (t) and each shock weakens the system making it more expensive to run. The long-run expected cost per unit time of running the system is obtained as well as the variance of the cost which are used to get optimal times of replacement of the system.

Keywords

NON-HOMOGENEOUS POISSON PROCESSCUMULATIVE DAMAGEPRODUCT DENSITIESOPTIMAL PERIODIC REPLACEMENTS
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 2 , June 1988 , pp. 375 - 382
Copyright
Copyright © Applied Probability Trust 1988 

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

Abdel-Hameed, M. (1984a) Life distribution properties of devices subject to a Levy wear process. Math. Operat. Res. 9, 606–614.Google Scholar
Abdel-Hameed, M. (1984b) Life distribution properties of devices subject to a pure jump damage process. J. Appl. Prob. 21, 816–825.CrossRefGoogle Scholar
Abdel-Hameed, M. (1986) Optimal replacement of a system subject to shocks. J. Appl. Prob. 23, 107–114.CrossRefGoogle Scholar
Feldman, R. M. (1976) Optimal replacement with semi-Markov shock models. J. Appl. Prob. 13, 108–117.Google Scholar
Gottlieb, G. (1982) Optimal replacement for shock models with general failure rate. Operat. Res. 30, 82–92.CrossRefGoogle Scholar
Gottlieb, G. and Levikson, B. (1984) Optimal replacement for self repairing shock models with general failure rate. J. Appl. Prob. 21, 108–119.Google Scholar
Ramakrishnan, A. (1950) Stochastic processes relating to particles distributed in a continuous infinity of states. Proc. Camb. Phil. Soc. 46, 595–602.CrossRefGoogle Scholar
Shanthikumar, J. G. and Sumita, U. (1983) General shock models associated with correlated renewal sequences. J. Appl. Prob. 20, 600–614.CrossRefGoogle Scholar
Srinivasan, S. K. (1974) Stochastic Point Processes and their Applications. Griffin, London.Google Scholar
Srinivasan, S. K., and Vasudevan, R. (1966) On a class of non-Markovian processes associated with correlated pulsetrains and their application to Barkhausen noise. Il Nuovo Cimento 41, 101–112.Google Scholar
Taha, H. A. (1982) Operations Research: An Introduction , 3rd edn. MacMillan, New York.Google Scholar
Zuckerman, D. (1978) Optimal stopping in a semi-Markov shock model. J. Appl. Prob. 15, 629–634.Google Scholar