Monte Carlo Analysis and Fuzzy Sets for Uncertainty Propagation in SIS Performance Assessment

Abstract

The object of this work is the probabilistic performance evaluation of safety instrumented systems (SIS), i.e. the average probability of dangerous failure on demand (PFDavg) and the average frequency of failure (PFH), taking into account the uncertainties related to the different parameters that come into play: failure rate (λ), common cause failure proportion (β), diagnostic coverage (DC)... This leads to an accurate and safe assessment of the safety integrity level (SIL) inherent to the safety function performed by such systems. This aim is in keeping with the requirement of the IEC 61508 standard with respect to handling uncertainty. To do this, we propose an approach that combines (1) Monte Carlo simulation and (2) fuzzy sets. Indeed, the first method is appropriate where representative statistical data are available (using pdf of the relating parameters), while the latter applies in the case characterized by vague and subjective information (using membership function). The proposed approach is fully supported with a suitable computer code. Keywords—Fuzzy sets, Monte Carlo simulation, Safety instrumented system, Safety integrity level.