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An inspection–repair–replacement model for a deteriorating system with unobservable state

Part of:Operations research and management scienceSpecial processes

Published online by Cambridge University Press:  14 July 2016

Lam Yeh
Lam Yeh*
Affiliation:
Northeastern University at Qinhuangdao and University of Hong Kong
*
∗ Postal address: Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong. Email address: ylam@hkustasc.hku.hk
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Abstract

In this paper, an inspection–repair–replacement (IRR) model for a deteriorating system with unobservable state is studied. Assume that the system state can only be diagnosed by inspection and an inspection is imperfect. After inspection, if the system is diagnosed as being in a down state, a minimal repair will be undertaken, otherwise we do nothing. Assume further that the system lifetime is a random variable having increasing failure rate. A feasible IRR policy is studied. An algorithm is then suggested for determining an optimal feasible IRR policy for minimizing the long-run average cost per unit time after a finite-step search.

Keywords

Minimal repairincreasing failure raterenewal reward processfeasible IRR policy

MSC classification

Primary:90B25: Reliability, availability, maintenance, inspection
Secondary:60K10: Applications (reliability, demand theory, etc.)

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 4 , September 2003, pp. 1031 - 1042
Copyright
Copyright © Applied Probability Trust 2003 

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References

Baker, R. D., and Christer, A. H. (1994). Operational research modelling of engineering aspects of maintenance. Europ. J. Operat. Res. 73, 407–422.CrossRefGoogle Scholar
Baker, R. D., and Wang, W. (1991). Determining the delay time distribution of faults in repairable machinery from failure data. IMA J. Math. Appl. Business Industry 3, 259–282.Google Scholar
Baker, R. D., and Wang, W. (1993). Developing and testing the delay time. J. Operat. Res. Soc. 33, 723–732.Google Scholar
Barlow, R. E., and Proschan, F. (1965). Mathematical Theory of Reliability. John Wiley, New York.Google Scholar
Butler, D. A. (1979). A hazardous-inspection model. Manag. Sci. 25, 79–89.CrossRefGoogle Scholar
Christer, A. H., and Waller, W. M. (1984a). Delay time models of industrial inspection maintenance problems. J. Operat. Res. Soc. 35, 401–406.CrossRefGoogle Scholar
Christer, A. H., and Waller, W. M. (1984b). An operational research approach to planned maintenance: modelling PM for vehicle fleet. J. Operat. Res. Soc. 35, 967–984.CrossRefGoogle Scholar
Christer, A. H., Wong, W., and Baker, R. D. (1995). Modelling maintenance practice of production plant using the delay-time concept. IMA J. Math. Appl. Business Industry 6, 67–83.Google Scholar
Ito, K., and Nakagawa, T. (1992). Optimal inspection policies for a system in storage. Comput. Math. Appl. 24, 87–90.CrossRefGoogle Scholar
Lam, Y. (1995). An optimal inspection—repair—replacement policy for standby systems. J. Appl. Prob. 32, 212–223.Google Scholar
Menke, J. T. (1983). Deterioration of electronics in store. In Proc. 28th Nat. SAMPE Symp. (April 1983), pp. 966–972.Google Scholar
Özekici, S., and Papazyan, T. (1988). Inspection policies and processes for deteriorating systems subject to catastrophic failure. Naval Res. Logistics 35, 481–492.3.0.CO;2-8>CrossRefGoogle Scholar
Özekici, S., and Pliska, S. R. (1991). Optimal scheduling of inspections: a delayed Markov model with false positives and negatives. Operat. Res. 39, 261–273.CrossRefGoogle Scholar
Ross, S. M. (1996). Stochastic Processes, 2nd edn. John Wiley, New York.Google Scholar
Thomas, L. C., Jacobs, P. A., and Gaver, D. P. (1987). Optimal inspection policies for standby systems. Commun. Statist. Stoch. Models 3, 259–273.CrossRefGoogle Scholar