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Optimal replacement under a minimal repair strategy—a general failure model

Published online by Cambridge University Press:  01 July 2016

Terje Aven
Terje Aven*
Affiliation:
University of Oslo
*
∗Postal address: Matematisk Institutt, Universitetet i Oslo, P.B. 1053 Blindern, Oslo 3, Norway.
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Abstract

In this paper we generalize the minimal repair replacement model introduced by Barlow and Hunter (1960). We assume that there is available information about the underlying condition of the system, for instance through measurements of wear characteristics and damage inflicted on the system. We assume furthermore that the system failure rate and the expected cost of a repair/replacement at any point of time are adapted to this information. At time t = 0 a new system is installed. At a stopping time T, based on the information about the condition of the system, the system is replaced by a new and identical one, and the process is repeated. Failures that occur before replacement are rectified through minimal repair. We assume that a minimal repair changes neither the age of the system nor the information about the condition of the system. The problem is to find a T which minimizes the total expected discounted cost. Under appropriate conditions an optimal T is found. Some generalizations and special cases are given.

Keywords

CONDITION-BASED MAINTENANCEREPLACEMENTMINIMAL REPAIRFAILURE RATEMINIMUM EXPECTED DISCOUNTED COST
Type
Research Article
Information
Advances in Applied Probability , Volume 15 , Issue 1 , March 1983 , pp. 198 - 211
Copyright
Copyright © Applied Probability Trust 1983 

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References

Aven, T. (1982) Optimal replacement times; a general set-up. Statistical Research Report, Institute of Mathematics, University of Oslo.Google Scholar
Barlow, R. E. and Hunter, L. (1960) Optimum preventive maintenance policies. Operat. Res. 1, 90–100.CrossRefGoogle Scholar
Barlow, E. E. and Proschan, F. (1965) Mathematical Theory of Reliability. Wiley, New York.Google Scholar
Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
Bergman, B. (1978) Optimal replacement under a general failure model. Adv. Appl. Prob. 10, 431–451.CrossRefGoogle Scholar
Bergman, B. (1980) On some recent advances in replacement theory. Society of Reliability Engineers Symposium, Chalmers Institute of Technology, Gothenberg, 5-6 May 1980.Google Scholar
Billingsley, P. (1979) Probability and Measure. Wiley, New York.Google Scholar
Dellacherie, C. and Meyer, P. A. (1978) Probabilities and Potential. North-Holland, Amsterdam.Google Scholar
Dynkin, E. B. (1965) Markov Processes, Vol. 1. Springer-Verlag, Berlin.Google Scholar
Grandell, J. (1975) Doubly Stochastic Poisson Processes. Lecture Notes in Mathematics 529, Springer-Verlag, Berlin.Google Scholar
Lamperti, J. (1977) Stochastic Processes. Springer-Verlag, New York.CrossRefGoogle Scholar
Meyer, P. A. (1966) Probability and Potentials. Blaisdell, Waltham, MA.Google Scholar
Muth, E. J. (1977) An optimal decision rule for repair vs. replacement. IEEE Trans. Reliability R-26, 179–181.CrossRefGoogle Scholar
Nakagawa, T. (1979) A summary of block replacement policies. RAIRO 4, 351–361.CrossRefGoogle Scholar
Nummelin, E. (1980) A general failure model: optimal replacement with state dependent replacement and failure costs. Math. Operat. Res. 3, 381–387.CrossRefGoogle Scholar
Phelps, R. I. (1981) Replacement policies under minimal repair. J. Operat. Res. Soc. 7, 549–554.CrossRefGoogle Scholar
Ross, S. (1969) Optimal dispatching of a Poisson process. J. Appl. Prob. 6, 692–699.CrossRefGoogle Scholar
Ross, S. (1971) Infinitesimal look ahead stopping rules. Ann. Statist. 1, 297–303.CrossRefGoogle Scholar
Serfozo, R. F. (1972) Conditional Poisson processes. J. Appl. Prob. 9, 288–303.CrossRefGoogle Scholar
Serfozo, R. F. (1972) Processes with conditional stationary independent increments. J. Appl. Prob. 9, 303–315.CrossRefGoogle Scholar
Torgersen, E. N. and Lindqvist, B. (1975) Notes on Comparison of Statistical Experiments. Statistical Memoirs, Institute of Mathematics, University of Oslo.Google Scholar
Yamada, K. (1981) Optimal stopping rules for jump processes. J. Math. Kyoto Univ. 1, 105–123.Google Scholar