Abstract
A method is proposed for the analytical evaluation of the cumulative failure probability distribution of complex repairable systems. The method is based on a set of integral equations each one referring to a specific minimal cut set of the system. Each integral equation links the unavailability of a minimal cut set to its failure probability density distribution and to the probability that the minimal cut set is down at time t under the condition that it was down at time t′ ( t′ ⩽ t). The limitations for the applicability of the method are also discussed. It has been concluded that the method is applicable if the process describing the failure of a minimal cut set is a ‘delayed semi-regenerative process’.
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