PFD Calculation of Multi-Channel Safety Functions Considering the Demand Rate

SUMMARY & CONCLUSIONSThe residual risk of safety-instrumented systems constitutes a critical non-functional requirement governed by international standards. One crucial measure is the probability of failure on demand (PFD), describing the likelihood of a safety function to be inoperable at the time when it is needed. Various approaches for quantifying safety as a function of key design parameters have been explored in the literature. However, existing methods often rely on simplifying assumptions, such as neglecting the effects of demands and proof tests, applying approximations, or restricting the analysis to the special cases of high or low demand. More complex scenarios are typically addressed using numerical techniques.This paper presents closed-form exact expressions for the average probability of failure on demand (PFD) in systems with redundant safety functions. The proposed formulas cover common multi-channel configurations, including 1oo2, 1oo3, and 2oo3 architectures, and are validated through comparison with detailed simulation results.