Markovian Reliability Analysis Under Uncertainty with an Application on the Shutdown System of the Clinch River Breeder Reactor

Abstract

A methodology for the assessment of uncertainties about reliability of nuclear reactor systems described by Markov models is developed, and the uncertainties about the failure probability of the shutdown system of the Clinch River Breeder Reactor (CRBR) are assessed. Failure and repair rates and all other inputs of reliability analysis are taken as random variables with known probability distribution functions (pdf's). The pdf of reliability is calculated by both a Monte Carlo simulation and a Taylor series expansion approximation. Three techniques are developed to reduce the computational effort: (a) ordering of system states, (b) merging of Markov processes, and (c) judicious choice of time steps. A Markov model has been used for reliability analysis under uncertainty of the shut down system of the CRBR. It accounts for common-cause failures, interdependences between unavailability of the system and occurrence of transients, and inspection and maintenance procedures that depend on the state of the system and that include possibility of human errors. Under these conditions, the failure probability of the shutdown system differs significantly from that computed without common-cause failures, human errors, and input uncertainties.

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