Probabilistic assessments in relationship with safety integrity levels by using Fault Trees

In this article, we study the assessment of safety integrity levels of safety-instrumented system by means of Fault Trees. We focus on functions with a low demand rate. For these functions, the appropriate measure of performance is the so-called probability of failure on demand (PFD) or probability of not functioning on demand. In order to calculate accurately the average PFD as per IEC 61508 standard, we introduce distributions for periodically tested components into Fault Tree models. We point out the specific problems raised by the assessment of safety integrity levels (SILs), which restrict the use of the formulae proposed in the standard. Among these problems there is the fact that SIL should be assessed by considering the time-dependent behavior of the system unavailability in addition to its average value. We check, on a simple pressure protection system, the results obtained by means of the Fault Tree approach against those obtained by means of stochastic Petri nets with predicates.