Evaluation of system reliability with common-cause failures, by a pseudo-environments model

An efficient method for calculating system reliability with CCFs (common-cause failures) is presented by applying the factoring (total probability) theorem when the system and its associated class of CCFs are both arbitrary. Existing methods apply this theorem recursively until no CCF remains to be considered, and so can be time-consuming in computation. The method applies such a theorem only once and can be carried out in two steps: (1) determine each state in terms of the occurrence (or not) of every CCF in the associated class, to regard it as a pseudo-environment and to calculate its probability or weight; (2) determine each resulting subsystem of the system under the environment, calculate its reliability as in the no CCF case and take the weighted sum of such reliabilities, viz, the system reliability. This method is in terms of a Markov process and requires only the occurrence rate of each CCF to obtain the probability of each environment and only the failure rate of each component to obtain the system reliability under each environment; hence, it is practical, efficient, and useful