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Multistate reliability models

Published online by Cambridge University Press:  14 July 2016

William S. Griffith
William S. Griffith*
Affiliation:
University of Pittsburgh
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Abstract

In this paper an axiomatic development of multistate systems is presented. Three types of coherence based on the strength of the relevancy axiom are studied. The strongest of these has been investigated previously by El-Neweihi, Proschan, and Sethuraman [3]. One of the weaker types of coherence permits wider applicability to real life situations without sacrificing any of the mathematical results obtained by El-Neweihi, Proschan, and Sethuraman. The concept of system performance is formalized through expected utility and the effect of component improvement on system performance is studied using a generalization of Birnbaum's reliability importance.

Keywords

RELIABILITYMULTISTATE COMPONENTSMULTISTATE COHERENT SYSTEMSCOMPONENT IMPORTANCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 3 , September 1980 , pp. 735 - 744
Copyright
Copyright © Applied Probability Trust 1980 

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References

[1] Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
[2] Barlow, R. E. and Wu, A. S. (1978) Coherent systems with multi-state components. Math. Operat, Res. 3, 275–281.CrossRefGoogle Scholar
[3] El-Neweihi, E., Proschan, F. and Sethuraman, J. (1978) Multistate coherent systems. J. Appl. Prob. 15, 675–688.CrossRefGoogle Scholar
[4] Ross, S. (1979) Multivalued state component systems. Ann. Prob. 7, 379–383.CrossRefGoogle Scholar