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

TL;DR

This paper challenges the traditional use of PFD for mitigation safety functions, proposing a PDF-based approach to better assess their reliability, supported by mathematical formulations and case studies.

Contribution

It introduces a novel methodology using PDF and expected failure degree as reliability metrics for mitigation safety functions, replacing PFD.

Findings

PFD is not suitable for mitigation SFs reliability assessment

The PDF-based approach provides a more accurate measure of failure risk

Case studies demonstrate practical applicability of the new method

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.