Probability bounds for series systems with variables constrained by sets of probability measures

Abstract

The paper first revisits the problem of finding bounds on the probability of failure of a series system when no information is available on the dependencies among modes' failure probabilities. Second, reliability bounds are calculated when input variables that control the modes' probability of failure are given as parameterised probability measures, random sets or p-boxes. The different meanings of independence for the input variables are folded into the formulation. It is determined when calculating the failure probability bounds for each failure mode and then calculating bounds for the system is advantageous with respect to directly calculating the system's probability of failure. The paper also shows how discretising given upper and lower CDF envelopes using the outer discretisation method (ODM) leads to validated bounds on the system's probability of failure.

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