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Improved bounds for the availability and unavailability in a fixed time interval for systems of maintained, interdependent components

Published online by Cambridge University Press:  01 July 2016

B. Natvig
B. Natvig*
Affiliation:
University of Oslo
*
∗Postal address: Matematisk Institutt, Universitetet i Oslo, Blindern Oslo 3, Norway.
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Abstract

In this paper we arrive at a series of bounds for the availability and unavailability in the time interval I = [tA, tB] ⊂ [0, ∞), for a coherent system of maintained, interdependent components. These generalize the minimal cut lower bound for the availability in [0, t] given in Esary and Proschan (1970) and also most bounds for the reliability at time t given in Bodin (1970) and Barlow and Proschan (1975). In the latter special case also some new improved bounds are given. The bounds arrived at are of great interest when trying to predict the performance process of the system. In particular, Lewis et al. (1978) have revealed the great need for adequate tools to treat the dependence between the random variables of interest when considering the safety of nuclear reactors.

Satyanarayana and Prabhakar (1978) give a rapid algorithm for computing exact system reliability at time t. This can also be used in cases where some simpler assumptions on the dependence between the components are made. It seems, however, impossible to extend their approach to obtain exact results for the cases treated in the present paper.

Keywords

AVAILABILITYUNAVAILABILITYBOUNDSFIXED TIME INTERVALMAINTENANCEINTERDEPENDENT COMPONENTS
Type
Research Article
Information
Advances in Applied Probability , Volume 12 , Issue 1 , March 1980 , pp. 200 - 221
Copyright
Copyright © Applied Probability Trust 1980 

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References

Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
Bodin, L. D. (1970) Approximations to system reliability using a modular decomposition. Technometrics 12, 335–344.Google Scholar
Esary, J. D. and Proschan, F. (1970) A reliability bound for systems of maintained, interdependent components. J. Amer. Statist. Assoc. 65, 329–338.Google Scholar
Lewis, H. et al. (1978) Risk assessment review group report for the U.S. Nuclear Regulatory Commission. Prepared for the U.S. Nuclear Regulatory Commission, Washington, D.C. 20555.Google Scholar
Satyanarayana, A. and Prabhakar, A. (1978) New topological formula and rapid algorithm for reliability analysis of complex networks. IEEE Trans. Reliability 27, 82–100.Google Scholar