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# Improved Bounds for the Availability and Unavailability in a Fixed Time Interval for Systems of Maintained, Interdependent Components

B. Natvig
Advances in Applied Probability
Vol. 12, No. 1 (Mar., 1980), pp. 200-221
DOI: 10.2307/1426502
Stable URL: http://www.jstor.org/stable/1426502
Page Count: 22
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## Abstract

In this paper we arrive at a series of bounds for the availability and unavailability in the time interval $I=[t_{A},t_{B}]\subset [0,\infty)$, 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.

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