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The purpose of this paper is to check the consistency of the IEC 61508 standard formula related to the average failure frequency (PFH: the probability of dangerous failure per hour) for a commonly used safety instrumented system (SIS) architecture in the process industry: 2-out-of-3 voting (2oo3), also known as Triple Modular Redundancy (TMR).

IEC 61508 standard provided PFH formulas for different SIS architectures, without explanations, assuming that the SIS puts the equipment under control into a safe state on the detection of dangerous failure. This assumption renders the use of classical reliability approaches such as fault trees and reliability block diagrams impractical for PFH calculation. That said, the consistency verification was performed thanks to a dynamic and flexible reliability approach, namely Markov chains following these steps: (1) developing the multi-phase Markov chains (MPMC) model for 2oo3 configuration, (2) deducing the related classical Markov chains (CMC) model and (3) deriving a new PFH formula for the 2oo3 architecture based on the CMC model and thoroughly comparing it to that given in the IEC 61508. Moreover, 2oo3 architecture has been modeled through Petri nets for numerical comparison purposes. That comparison has been carried out between the numerical results obtained from IEC 61508 formula, the newly derived formula, Markov chains and Petri nets models.

The newly obtained formula for 2oo3 configuration contains extra terms compared with the IEC 61508 one. Therefore, this latter formula induces an underestimated PFH results, which is dangerous from a safety point of view. This fact was corroborated by the numerical comparison.

This paper does not consider the different configurations given in IEC 61508.

In our knowledge, no verification works have been conducted before on the IEC 61508 PFH formulas with shutdown capability. Therefore, the nonaccuracy of the PFH formula related to the 2oo3 has not been stated before. This paper proposes a new and more accurate formula.

This study aims to improve the reliability of emergency safety barriers by using the subjective safety analysis based on evidential reasoning theory in order to develop on a framework for optimizing the reliability of emergency safety barriers.

The emergency event tree analysis is combined with an interval type-2 fuzzy-set and analytic hierarchy process (AHP) method. In order to the quantitative data is not available, this study based on interval type2 fuzzy set theory, trapezoidal fuzzy numbers describe the expert's imprecise uncertainty about the fuzzy failure probability of emergency safety barriers related to the liquefied petroleum gas storage prevent. Fuzzy fault tree analysis and fuzzy ordered weighted average aggregation are used to address uncertainties in emergency safety barrier reliability assessment. In addition, a critical analysis and some corrective actions are suggested to identify weak points in emergency safety barriers. Therefore, a framework decisions are proposed to optimize and improve safety barrier reliability. Decision-making in this framework uses evidential reasoning theory to identify corrective actions that can optimize reliability based on subjective safety analysis.

A real case study of a liquefied petroleum gas storage in Algeria is presented to demonstrate the effectiveness of the proposed methodology. The results show that the proposed methodology provides the possibility to evaluate the values of the fuzzy failure probability of emergency safety barriers. In addition, the fuzzy failure probabilities using the fuzzy type-2 AHP method are the most reliable and accurate. As a result, the improved fault tree analysis can estimate uncertain expert opinion weights, identify and evaluate failure probability values for critical basic event. Therefore, suggestions for corrective measures to reduce the failure probability of the fire-fighting system are provided. The obtained results show that of the ten proposed corrective actions, the corrective action “use of periodic maintenance tests” prioritizes reliability, optimization and improvement of safety procedures.

This study helps to determine the safest and most reliable corrective measures to improve the reliability of safety barriers. In addition, it also helps to protect people inside and outside the company from all kinds of major industrial accidents. Among the limitations of this study is that the cost of corrective actions is not taken into account.

Our contribution is to propose an integrated approach that uses interval type-2 fuzzy sets and AHP method and emergency event tree analysis to handle uncertainty in the failure probability assessment of emergency safety barriers. In addition, the integration of fault tree analysis and fuzzy ordered averaging aggregation helps to improve the reliability of the fire-fighting system and optimize the corrective actions that can improve the safety practices in liquefied petroleum gas storage tanks.