Uncertainty handling in safety instrumented systems according to IEC 61508 and new proposal based on coupling Monte Carlo analysis and fuzzy sets

Safety instrumented systems must be designed, built and operated to meet tolerable risk level as required regulatory agencies. This requirement is closely related to their probabilistic performance measures which are either their average probability of dangerous failure on demand (PFDavg) or their average frequency of failure (PFH: Probability of Failure per Hour). The object of this work is the SIS performances evaluation 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), etc. This leads to an accurate and therefore safe assessment of the safety integrity level (SIL) inherent to safety functions performed by such systems. This aim is in keeping with the requirement of the IEC 61508 standard with respect to handling uncertainty. In this paper we first explain in detail the IEC 61508 approach for handling uncertainty. Afterwards, we propose an approach that combines (i) Monte Carlo analysis (MCA) and (ii) fuzzy sets. Indeed, the first method is appropriate when 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 developed under the MATLAB environment.