New insight into the average probability of failure on demand and the probability of dangerous failure per hour of safety instrumented systems

The aim of this paper is to give a new insight into some fundamental concepts of the IEC 61508 standard. First, low and high or continuous demand modes of operation of safety instrumented systems are examined by analysing their official definitions given in the IEC 61508 and IEC 61511 standards. In this context, the paper proposes a new criterion for distinguishing these two modes of operation. A study allowing the determination of accident frequency is also presented, where the system under study consists of one element under control and its associated safety instrumented system. Second, the relationship between the average probabilities of failure on demand and the risk reduction factor is studied. It is shown that the commonly used approach (the standard approach) may lead to an optimistic value for the risk reduction factor. Finally, the paper clarifies the nature of the probability of failure per hour of a safety instrumented system and proposes different ways to compute this in the general case, bas...