Boolean algebra method to calculate network system reliability indices in terms of a proposed FMEA

Abstract

As different MC's or MP's (minimal cuts or paths) may have common components, we cannot apply the product rule to evaluate the system reliability through the RBD (reliability block diagram) of MC's. However, for a non-oriented network, the series of MC's up to order 2 can be transformed into the series of independent parallel-series, i.e. having no common components between each other. Hence, for a very reliable network such as a power station, such a series can be approximately regarded as its RBD so that the product rule, that the system availability is the product of those of independent blocks, applies. For a highly reliable network such as a power transmission and distribution system, more MC's up to an order say 3,4 or even the upmost one should be taken into account. The product rule still applies if we further apply the pivotal decomposition formulas. The method to calculate the system failure frequency is developed in parallel. In terms of the similar ‘differential and integral’ relationship between the failure frequency and the availability, we can easily derive the failure frequency from the availability. For a network with a few oriented arcs, we have to pivot on such arcs first.