Probability and frequency calculations related to protection layers revisited

• The quantification of failure frequency of safety-related systems is performed.
• The concept of independent layers of protection is not as obvious as it appears.
• A procedure carried out by using an adapted fault tree model is proposed.
• In many cases the use of models with a wider representation power (Markov model, Petri Nets) is required.

This article casts a new glance over some methods dedicated to the calculation of the likelihood (probability or frequency) of failure of systems and, in particular, safety-related systems working alone or in association with other protection layers. It consists first in examining with a critical eye the relevancy of the aforementioned methods, which are still often used in spite of their restrictive limitations, and second in proposing an alternative approach for each of them. The correctness of the examinated methods is tested by applying them to very simple systems modeled by fault tree models, with intent to show why these methods are debatable and how they can be replaced by other ones, more appropriate. The particular case of several protection layers having to react on the demand resulting from the global failure of their associated control system is considered. That case leads to revisit the common assumption of the independence between the above protection layers and control system, by taking into account the order of their respective failures from a qualitative and quantitative point of view.