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Optimal allocation of resources to nodes of parallel and series systems

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  01 July 2016

Moshe Shaked  and
J. George Shanthikumar
Moshe Shaked*
Affiliation:
University of Arizona
J. George Shanthikumar*
Affiliation:
University of California, Berkeley
*
∗Postal address: Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA.
∗∗Postal address: Walter A. Haas School of Business, University of California, Berkeley, CA 94720, USA.
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Abstract

In this paper we consider parallel and series systems, the components of which can be ‘improved'. The ‘improvement' consists of supplying the components with cold or hot standby spares or by allotting to them fixed budgets for minimal repairs. A fixed total resource of spares or minimal repairs is available. We find the optimal allocation of the resource items in several commonly encountered settings.

Keywords

MINIMAL REPAIRSHOT AND COLD STANDBY SPARESOPTIMAL RESOURCE ALLOCATIONMAJORIZATION, SCHUR-CONVEXITY AND CONCAVITYSTOCHASTIC ORDERLIKELIHOOD RATIO ORDERINCREASING FAILURE RATELOGCONCAVITYNON-HOMOGENEOUS POISSON PROCESSRELIABILITY THEORY

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Advances in Applied Probability , Volume 24 , Issue 4 , December 1992 , pp. 894 - 914
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

Research supported by the Air Force Office of Scientific Research, USAF, under Grant AFOSR-84–0205.

References

Arjas, E. and Norros, I. (1989) Changes of life distribution via a hazard transformation: An inequality with application to minimal repair. Math. Operat. Res. 14, 355–361.CrossRefGoogle Scholar
Ascher, H. and Feingold, H. (1984) Repairable Systems Reliability. Decker, New York.Google Scholar
Barlow, R. E. and Brunk, H. D. (1972) The isotonic regression problem with its dual. J. Amer. Statist. Assoc. 67, 140–147.CrossRefGoogle Scholar
Barlow, R. E. and Hunter, L. (1960) Optimum preventive maintenance policies. Operat. Res. 8, 90–100.CrossRefGoogle Scholar
Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
Baxter, L. A. and Harche, F. (1990) On the optimal assembly of series-parallel systems. New York University Technical Report SOR-90–12.Google Scholar
Boland, P. J., El-Neweihi, E. and Proschan, F. (1988) Active redundancy allocation in coherent systems. Prob. Eng. Inf. Sci. 2, 343–353.Google Scholar
Boland, P. J., El-Neweihi, E. and Proschan, F. (1990) Stochastic order for redundancy allocation in series and parallel systems. Adv. Appl. Prob. 24, 161–171.Google Scholar
Boland, P. J., El-Neweihi, E. and Proschan, F. (1991) Redundancy importance and allocation of spares in coherent systems. J. Statist. Planning Inf. 29, 55–66.CrossRefGoogle Scholar
Derman, C., Lieberman, G. J. and Ross, S. M. (1974) Assembly of systems having maximum reliability. Naval. Res. Logist. Quart. 21, 1–12.CrossRefGoogle Scholar
El-Neweihi, E., Proschan, F. and Sethuraman, J. (1986) Optimal allocation of components in parallel-series and series-parallel systems. J. Appl. Prob. 23, 770–777.CrossRefGoogle Scholar
Esary, J. D., Marshall, A. W. and Proschan, F. (1973) Shock models and wear processes. Ann. Prob. 1, 627–649.CrossRefGoogle Scholar
Karlin, S. (1968) Total Positivity. Stanford University Press, Stanford CA.Google Scholar
Marshall, A. W. and Olkin, I. (1979) Inequalities: Theory of Majorization and Its Applications . Academic Press, New York.Google Scholar
Natvig, B. (1990) On information-based minimal repair and the reduction in remaining system lifetime due to the failure of a specific module. J. Appl. Prob. 27, 365–375.Google Scholar
Robertson, T. and Wright, F. T. (1982) On measuring the conformity of a parameter set to a trend, with applications. Ann. Statist. 10, 1234–1245.CrossRefGoogle Scholar
Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar
Shanthikumar, J. G. and Yao, D. D. (1986) The preservation of likelihood ratio ordering under convolution. Stoch. Proc. Appl. 23, 259–267.CrossRefGoogle Scholar
Shanthikumar, J. G. and Yao, D. D. (1991) Bivariate characterization of some stochastic order relations. Adv. Appl. Prob. 23, 642–659.CrossRefGoogle Scholar