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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. [ABSTRACT FROM AUTHOR]

• A new model for the safety measures optimal selection. • Different combination of objective function are introduced. • The priority of objective functions are modelled by lexicographic approach. • A pessimistic strategy to consider the synergistic effects of safety measures. • A multi-objective genetic algorithm with NSGA II technique is developed to solve the optimization problem. Optimal selection of safety measures (SMs) is a challenging task for safety managers due to its importance, complexity, and incapability of traditional approaches in considering all the aspects of SMs optimal selection. Sophisticated mathematical models can be used to overcome the limitations of traditional approaches. However, setting the objective functions while considering their priorities as well as possible synergistic effects of the SMs on the hazards are still among the main concerns in the development and application of mathematical models. The present study is aimed at developing a methodology to optimize the SMs selection while addressing the aforementioned challenges and considering both the budget and the risks. To do so, first the Pareto set of the solutions is obtained by NSGA-II technique - a multi-objective genetic algorithm technique - where a lexicographic model is used to select the optimal solution from the Pareto set based on the priority of the objective functions. A pessimistic strategy is used to account for the synergistic effects and the overlaps between the selected SMs. Two mathematical models are developed to represent different policies in optimal SMs selection in a gas wellhead and surface facility. The results show a notable difference between the two policies, indicating the importance of setting proper objective functions in multi-objective optimization problems. The results also show that the methodology is able to effectively satisfy different safety management policies and constraints with no need for much extra information except the cost and impact of SMs on the hazards' risk. [ABSTRACT FROM AUTHOR]