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Optimal replacement times — a general set-up

Published online by Cambridge University Press:  14 July 2016

Terje Aven  and
Bo Bergman
Terje Aven
Affiliation:
University of Oslo
Bo Bergman*
Affiliation:
Linköping Institute of Technology
*
∗∗Postal address: Linköping Institute of Technology, S-58188 Linköping, Sweden.
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Abstract

For a large class of replacement models for stochastically deteriorating systems the optimality criteria of total expected discounted cost and long-run (expected) average cost per unit time have a common structure. In the present paper a formal description of this structure is given and the optimal rule is determined. A so-called ‘λ -minimization technique' is applied. This method is discussed in general terms.

Keywords

AVERAGE COSTEXPECTED DISCOUNTED COSTSTOPPING TIMEOPTIMIZATIONλ-PROBLEMS
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 2 , June 1986 , pp. 432 - 442
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

∗

Present address: Rogaland College, P.O. Box 2540, Ullandhaug, 4001 Stavanger, Norway.

References

Abdel-Hameed, M. and Shimi, I. N. (1978) Optimal replacement of damaged devices. J. Appl. Prob. 15, 153–161.Google Scholar
Ash, R. B. (1972) Real Analysis and Probability. Academic Press, New York.Google Scholar
Aven, T. (1983a) Optimal replacement under a minimal repair strategy — a general failure model. Adv. Appl. Prob. 15, 198–211.Google Scholar
Aven, T. (1983b) Contributions to Failure Time Data Analysis and Optimal Maintenance Planning. , University of Oslo.Google Scholar
Barlow, R. E. and Proschan, F. (1965) Mathematical Theory of Reliability. Wiley, New York.Google Scholar
Bergman, B. (1978) Optimal replacement under a general failure model. Adv. Appl. Prob. 10, 431–451.Google Scholar
Bergman, B. (1980) On some recent advances in replacement theory. From the Society of Reliability Engineers symposium “Tillforlighetsdagar på Chalmars 5.–6. mai 1980”, Chalmers Institute of Technology, Gothenburg.Google Scholar
Conte, S. D. and De Boor, C. (1972) Elementary Numerical Analysis. McGraw-Hill Kogakusha, Tokyo.Google Scholar
Meyer, P. A. (1966) Probability and Potentials. Blaisdell, Waltham, Mass.Google Scholar
Nummelin, E. (1980) A general failure model: Optimal replacement with state dependent replacement and failure costs. Math. Operat. Res. 3, 381–387.Google Scholar
Ross, S. (1971) Infinitesimal look-ahead stopping rules. Ann. Math. Statist. 42, 297–303.Google Scholar
Taylor, H. M. (1975) Optimal replacement under additive damage and other failure models. Naval Res. Logist. Quart. 22, 1–18.Google Scholar
Yamada, K. (1980) Explicit formula of optimal replacement under additive shock processes. Stoch. Proc. Appl. 9, 193–208.Google Scholar
Zuckerman, D. (1978a) Optimal replacement policy for the case where damage process is a one-sided Lévy process. Stoch. Proc. Appl. 7, 141–151.Google Scholar
Zuckerman, D. (1978b) Optimal stopping in a semi-Markov shock model. J. Appl. Prob. 15, 629–634.Google Scholar
Zuckerman, D. (1979) Optimal replacement rule-discounted cost criterion. RAIRO 1, 67–74.Google Scholar