Assessment of the expected number and frequency of failures of periodically tested systems

The safety and reliability analysis of any system necessarily requires first to model its behavior or its failure logic, and second to assess its performance by using the previously chosen model. Among these performance indicators there is the failure frequency. In spite of its interest, it is not very often used, except in the standards devoted to the so-called functional safety, in which its genuine nature is not always made explicit. A sound method dedicated to the modeling and computing of the failure frequency of periodically tested systems is proposed in this paper. This type of systems comprises components with an availability curve which is discontinuous at deterministic instants. These discontinuities induce, in turn and at the same instants, frequency discontinuities. The impact of the latter on the overall value of the failure frequency is important, but largely unknown and therefore not taken into account in the safety and reliability area, in spite of the fact that it generally induces optimistic estimation, if no compensatory action is planned. The presented method is based on the notion of “critical state” and the use of advanced fault tree models (FT). The results obtained from these models are checked by using Monte Carlo simulation technique supported by equivalent Petri nets models (PN).