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Optimal replacement under a general failure model

Published online by Cambridge University Press:  01 July 2016

Bo Bergman
Bo Bergman*
Affiliation:
Saab-Scania AB, Linkoping and University of Lund
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Abstract

Replacement policies based on measurements of some increasing state variable, e.g. wear, accumulated damage or accumulated stress, are studied in this paper. It is assumed that the state measurements may be regarded as realizations of some stochastic process and that the proneness to failure of an active unit may be described by an increasing state-dependent failure rate function. Average long-run cost per unit time is considered. The optimal replacement rule is shown to be a control limit rule, i.e. it is optimal to replace either at failure or when the state variable has reached some threshold value, whichever occurs first. The optimal rule is determined. Some generalizations and special cases are given.

Keywords

REPLACEMENTMAINTENANCE ON CONDITIONFAILURE RATESTATE MEASUREMENTSSTOCHASTIC WEARSTOCHASTIC PROCESSESOPTIMIZATION
Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 2 , June 1978 , pp. 431 - 451
Copyright
Copyright © Applied Probability Trust 1978 

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References

Antelman, G. and Savage, I. R. (1965) Characteristic functions of stochastic integrals and reliability theory. Naval Res. Logist. Quart. 12, 199–222.Google Scholar
Barlow, R. 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
Cherniavsky, E. A. (1973) Some Contributions to Failure Models: The Shock and Continuous Danger Model. , Cornell University.Google Scholar
Çinlar, E. (1975) Introduction to Stochastic Processes. Prentice Hall, Englewood Cliffs, N.J.Google Scholar
Cox, D. R. (1962) Renewal Theory. Methuen, London.Google Scholar
Derman, C. and Sacks, J. (1960) Replacement of periodically inspected equipment. Naval Res. Logist. Quart. 7, 597–607.Google Scholar
Feldman, R. M. (1976) Optimal replacement with semi-Markov shock models. J. Appl. Prob. 13, 108–117.Google Scholar
Gaver, D. P. (1963) Random hazard in reliability problems. Technometrics 5, 211–225.CrossRefGoogle Scholar
Grandell, J. (1975) Doubly stochastic Poisson processes. Institute of Actuarial Mathematics and Mathematical Statistics, University of Stockholm, Research Report No. 102.Google Scholar
Kao, E. P. E. (1973) Optimal replacement rules when changes of state are semi-Markovian. Opns Res. 21, 1231–1249.Google Scholar
Luss, H. (1976) Maintenance policies when deterioration can be observed by inspections. Opns Res. 24, 359–366.Google Scholar
Mercer, A. (1961) Some simple wear-dependent renewal processes. J. R. Statist. Soc. B 23, 368–376.Google Scholar
Reynolds, D. S. and Savage, I. R. (1971) Random wear models in reliability theory. Adv. Appl. Prob. 3, 229–248.CrossRefGoogle Scholar
Ross, S. M. (1971) Infinitesimal-look-ahead stopping rules. Ann. Math. Statist. 42, 297–303.CrossRefGoogle Scholar
Taylor, H. M. (1975) Optimal replacement under additive damage and other failure models. Naval Res. Logist. Quart. 22, 1–18.CrossRefGoogle Scholar