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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.

The main objective of safety instrumented systems (SISs) is to maintain a safe condition of a facility if hazardous events occur. However, in some cases, SIS's can be activated prematurely, these activations are characterized in terms of frequency by a Spurious Trip Rate (STR) and their occurrence leads to significant technical, economic and even environmental losses. This work aims to propose an approach to optimize the performances of the SIS by a multi-objective genetic algorithm. The optimization of SIS performances is performed using the multi-objective genetic algorithm by minimizing their probability of failure on demand PFDavg, Spurious Trip Rate (STR) and Life Cycle Costs (LCCavg). A set of constraints related to maintenance costs have been established. These constraints imply specific maintenance strategies which improve the SIS performances and minimize the technical, economic and environmental risks related to spurious shutdowns. Validation of such an approach is applied to an Emergency Shutdown (ESD) of the blower section of an industrial facility (RGTE- In Amenas).

The optimization of SIS performances is performed using the multi-objective genetic algorithm by minimizing their probability of failure on demand PFDavg, Spurious Trip Rate (STR) and Life Cycle Costs (LCCavg). A set of constraints related to maintenance costs have been established. These constraints imply specific maintenance strategies which improve the SIS performances and minimize the technical, economic and environmental risks related to spurious shutdowns. Validation of such an approach is applied to an Emergency Shutdown (ESD) of the blower section of an industrial facility (RGTE- In Amenas).

A case study concerning a safety instrumented system implemented in the RGTE facility has shown the great applicability of the proposed approach and the results are encouraging. The results show that the selection of a good maintenance strategy allows a very significant minimization of the PFDavg, the frequency of spurious trips and Life Cycle Costs of SIS.

The maintenance strategy defined by the system designer can be modified and improved during the operational phase, in particular safety systems. It constitutes one of the least expensive investment strategies for improving SIS performances. It has allowed a considerable minimization of the SIS life cycle costs; PFDavg and the frequency of spurious trips.