Probability of Loss of Assured Safety in Systems with Multiple Time-Dependent Failure Modes: Representations with Aleatory and Epistemic Uncertainty.

Weak link (WL)/strong link (SL) systems are important parts of the overall operational design of high-consequence systems. In such designs, the SL system is very robust and is intended to permit operation of the entire system under, and only under, intended conditions. In contrast, the WL system is intended to fail in a predictable and irreversible manner under accident conditions and render the entire system inoperable before an accidental operation of the SL system. The likelihood that the WL system will fail to deactivate the entire system before the SL system fails (i.e., degrades into a configuration that could allow an accidental operation of the entire system) is referred to as probability of loss of assured safety (PLOAS). Representations for PLOAS for situations in which both link physical properties and link failure properties are time-dependent are derived and numerically evaluated for a variety of WL/SL configurations, including PLOAS defined by (i) failure of all SLs before failure of any WL, (ii) failure of any SL before failure of any WL, (iii) failure of all SLs before failure of all WLs, and (iv) failure of any SL before failure of all WLs. The indicated formal representations and associated numerical procedures for the evaluation of PLOAS are illustrated with example analyses involving (i) only aleatory uncertainty, (ii) aleatory uncertainty and epistemic uncertainty, and (iii) mixtures of aleatory uncertainty and epistemic uncertainty.