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More on optimal allocation of components in coherent systems

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

Published online by Cambridge University Press:  14 July 2016

Fan C. Meng
Fan C. Meng*
Affiliation:
Academia Sinica
*
∗Postal address: Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan.
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Abstract

More applications of the principle for interchanging components due to Boland et al. (1989) in reliability theory are presented. In the context of active redundancy improvement we show that if two nodes are permutation equivalent then allocating a redundancy component to the weaker position always results in a larger increase in system reliability, which generalizes a previous result due to Boland et al. (1992). In the case of standby redundancy enhancement, we prove that a series (parallel) system is the only system for which standby redundancy at the component level is always more (less) effective than at the system level. Finally, the principle for interchanging components is extended from binary systems to the more complicated multistate systems.

Keywords

COHERENT SYSTEMACTIVE REDUNDANCYSTANDBY REDUNDANCYSTOCHASTIC ORDERLIKELIHOOD RATIO ORDERMULTISTATE SYSTEM

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 2 , September 1996 , pp. 548 - 556
Copyright
Copyright © Applied Probability Trust 1996 

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References

Barlow, R. E. and Proschan, F. (1975) Importance of system components and fault tree events. Stock. Proc. Appl. 3, 153–173.CrossRefGoogle Scholar
Barlow, R. E. and Proschan, F. (1981) Statistical Theory of Reliability and Life Testing. To Begin With, Silver Spring, MD.Google Scholar
Barlow, R. E. and Wu, A. S. (1978) Coherent systems with multistate components. Math. Operat. Res. 4, 275–281.Google Scholar
Birnbaum, Z. W. (1969) On the importance of different components in a multicomponent system. In Multivariate Analysis-II. pp. 581–592. ed. Krishnaiah, P. R. Academic Press, New York.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. (1991) Redundancy importance and allocation of spares in coherent systems. J. Statist. Planning Inf. 29, 55–66.Google Scholar
Boland, P. J., El-Neweihi, E. and Proschan, F. (1992) Stochastic order for redundancy allocation in series and parallel systems. Adv. Appl. Prob. 24, 161–171.Google Scholar
Boland, P. J. and Proschan, F. (1994) Stochastic order in system reliability theory. In Stochastic Orders and Their Applications. pp. 485–508. ed. Shaked, M. and Shanthikumar, J. G. Academic Press, New York.Google Scholar
Boland, P. J., Proschan, F. and Tong, Y. L. (1989) Optimal arrangement of components via pairwise rearrangements. Naval Res. Logist. 36, 807–815.Google Scholar
El-Neweihi, E. and Proschan, F. (1984) Degradable systems: A survey of multistate system theory. Commun. Statist. A: Theor. Meth. 13, 405–432.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
Esary, J. D. and Marshall, A. W. (1970) Coherent life functions. SIAM J. Appl. Math. 18, 810–814.Google Scholar
Meng, F. C. (1994) Comparing criticality of nodes via minimal cut (path) sets for coherent systems. Prob. Eng. Inf. Sci. 8, 79–87.Google Scholar
Meng, F. C. (1995) Some further results on ranking the importance of system components. Reliab. Eng. Syst. Safety. 47, 97–101.CrossRefGoogle Scholar
Natvig, B. (1982) Two suggestions of how to define a multistate coherent system. Adv. Appl. Prob. 14, 434–455.Google Scholar
Ross, S. (1983) Stochastic Processes. Wiley, New York.Google 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.Google Scholar
Shen, K. and Xie, M. (1991) The effectiveness of adding standby redundancy at system and component levels. IEEE Trans. Reliab. 40, 53–55.Google Scholar