A risk-based fuzzy arithmetic model to determine safety integrity levels considering individual and societal risks

Risk-based techniques such as risk graph and Layer of Protection Analysis (LOPA) are used to determine the Safety Integrity Level (SIL) of safety instrumented functions to ensure that risk is reduced to a tolerable level. However, these techniques have some drawbacks. For instance, they need absolute and precise numbers to evaluate SIL parameters, which are rarely available or are highly uncertain. In addition, they are incapable of considering individual and societal risks simultaneously. Moreover, risk tolerance criteria are likely to be used incorrectly in the LOPA technique, and risk graph is difficult to calibrate. In the current paper, a novel comprehensive fuzzy arithmetic model has been developed to determine the required SILs in process industries. The fuzzy required Risk Reduction Factor (RRF) is calculated for both individual and societal risks. Fuzzy numbers are developed from crisp intervals, based on the expected interval of the fuzzy numbers. Expert fuzzy-scaled elicitation has been applied to obtain the SIL parameters. In the proposed model, the overall risk tolerance criterion and apportionment factor are defined as SIL parameters for both individual and societal risks to ensure that the applied risk criteria are compliant with the requirements of the system. In addition, an approach is introduced for determining the required SIL based on the fuzzy required RRF. The proposed methodology was demonstrated to alleviate the limitations, and thus, can be considered as a more precise alternative to the conventional methods.