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Optimal active redundancy allocation in k-out-of-n system

Part of: Operations research and management science Survival analysis and censored data

Published online by Cambridge University Press:  14 July 2016

Jie Mi
Jie Mi*
Affiliation:
Florida International University
*
∗Postal address: Department of Statistics, Florida International University, University Park, Miami, FL 33199, USA. Email address: mi@fiu.edu.
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Abstract

A k-out-of-n system consisting of n components is one that works if and only if at least k of the n components work. Suppose there are n+r (1 ≤ r ≤ n) components available of which r will be used for active redundancy. From the given n+r components, r components are chosen to be used as active redundancies, and another r components receive active redundancies (i.e. these r components are bolstered). Consider a k-out-of-n system consisting of the r bolstered and the other n – r original components. The problem of which r components should be used for active redundancy, and where to allocate them in order to maximize the lifetime of the resulting k-out-of-n system is studied. It is shown that under the usual stochastic ordering ‘≤st’ the first r weakest components should be used for active redundancy and allocated in reverse order to the next r weakest components.

Keywords

Active redundancystochastic orderingk-out-of-n system

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 90B25: Reliability, availability, maintenance, inspection
Type
Short Communications
Information
Journal of Applied Probability , Volume 36 , Issue 3 , September 1999 , pp. 927 - 933
Copyright
Copyright © Applied Probability Trust 1999 

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References

Boland, P. J., El-Neweihi, E., and Proschan, F. (1988). Active redundancy allocation in coherent systems. Prob. Eng. Inf. Sci. 2, 343–353.CrossRefGoogle Scholar
Boland, P. J., El-Neweihi, E., and Proschan, F. (1991). Redundancy importance and allocation of spares in coherent systems. J. Statist. Plann. Inf. 29, 55–66.CrossRefGoogle Scholar
Boland, P. J., El-Neweihi, E., and Proschan, F. (1992). Stochastic order for redundancy allocations in series and parallel systems. Adv. Appl. Prob. 24, 161–171.CrossRefGoogle Scholar
El-Neweihi, E., and Sethuraman, J. (1993). Optimal allocation under partial ordering of lifetimes of components. Adv. Appl. Prob. 25, 914–925.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
Shaked, M., and Shanthikumar, J. G. (1992). Optimal allocation of resources to nodes of parallel and series systems. Adv. Appl. Prob. 24, 894–914.CrossRefGoogle Scholar
Shaked, M., and Shanthikumar, J. G. (1994). Stochastic Orders and Their Applications. Academic Press, New York.Google Scholar
Singh, H., and Misra, N. (1994). On redundancy allocations in systems. J. Appl. Prob. 31, 1004–1014.CrossRefGoogle Scholar