Reliability Analysis of k-out-of-n Systems of Components with Potentially Brittle Behavior by Universal Generating Function and Linear Programming

Due to initial cracks, careless construction, and extreme load conditions, components with brittle behavior may exist in a structural system. The presence of brittle behavior of components usually is accompanied by a low strength. However, existing methods for calculating the reliability of structures of components with brittle behavior are rather complicated or impossible. By means of decomposing the entire system into a set of subsystems, this paper proposed a method to estimate the bounds on failure probability of k-out-of-n system of components with potentially brittle behavior by using universal generating function (UGF) and linear programming (LP). Based on the individual component state probabilities and joint probabilities of the states of a small number of components, the proposed method can provide the bounds for the failure probability of a system with a large number of components. The accuracy and efficiency of the proposed method are investigated using numerical examples.

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