A mathematical optimization model for determining safety integrity levels in process facilities

In process industries, Safety Instrumented Functions (SIFs) are implemented to meet government-mandated risk tolerance criteria, which aim to ensure the safety of both individuals and society. The level of risk reduction achieved by a SIF is quantified by its Safety Integrity Level (SIL). Determining the target SILs is a challenging task for facility owners as they must balance the costs and benefits of risk reduction while complying with regulatory requirements. Furthermore, governments define risk tolerance criteria for an overall facility rather than for single scenarios. Therefore, determining a set of SILs for all SIFs becomes imperative to collectively reduce both individual and societal risks to tolerable levels intended for the overall facility. In this paper, we propose a mathematical optimization model to determine the most beneficial collection of SILs that guarantees meeting the risk tolerance criteria. Our model considers both individual and societal risk perspectives and effectively models an overall facility. The proposed model is applied to a process facility and the results are compared with the results from the existing methods for SIL determination. The results demonstrate the model's superior effectiveness in helping owners to select the most beneficial target SILs while ensuring compliance with government requirements.