PFD calculation method for systems with high failure rates, long test intervals, and many components

Safety Instrumented Functions (SIFs) in low-demand mode are key elements of risk reduction in the process industry. Their performance is commonly expressed through the average probability of failure on demand (PFD), forming the basis for compliance with Safety Integrity Level (SIL) targets. Current calculation methods, such as those presented in IEC 61508 and the PDS Method Handbook, rely on simplified formulas under a set of assumptions. For systems with high failure rates, long proof test intervals, or a large number of components, some of these assumptions are violated. When λ·τ is not "small enough," the resulting approximations may become overly conservative and, in some cases, produce unrealistic values (e.g., PFD > 100 % ). Although such systems fall outside the applicability of IEC 61508 and IEC 61511 as they cannot meet even the lowest SIL 1 requirement, other guidelines (e.g., OG 00046) recognize the need to manage safety functions with requirements below SIL 1. We propose a revised PFD calculation methodology which builds on the PDS Method framework but relaxes assumptions such as linearization of the time-dependent probability of failure on demand PFD(t) and the negligibility of simultaneous independent failures. The method offers improved validity for challenging cases while remaining considerably simpler than advanced approaches such as Markov models, yet more accurate and interpretable than current simplified formulas. Numerical examples illustrate the differences between the proposed method and current simplified formulas, highlighting the importance of extending the validity range for reliability assessments. The revised methodology bridges the gap between theoretical rigor and practical usability, providing a basis for consistent management of all instrumented safety functions, irrespective of SIL.

Keywords: Probability of failure on demand (PFD), Reliability assessment, High failure rates, Long test intervals.