PFD or PDF: Rethinking the Probability of Failure in Mitigation Safety Functions

Abstract: SIL (Safety Integrity Level) allocation plays a crucial role in defining the design requirements for Safety Functions (SFs) within high-risk industries. SIL is typically determined based on the estimated Probability of Failure on Demand (PFD), which must remain within permissible limits to manage risk effectively. Extensive research has been conducted on determining target PFD and SIL, with a stronger emphasis on preventive SFs than on mitigation SFs. In this paper, we address a rather conceptual issue: we argue that PFD is not an appropriate reliability measure for mitigation SFs to begin with, and we propose an alternative approach that leverages the Probability Density Function (PDF) and the expected degree of failure as key metrics. The principles underlying this approach are explained and supported by detailed mathematical formulations. Furthermore, the practical application of this new methodology is illustrated through case studies.