Interaction effects of multiple input parameters on the integrity of safety instrumented systems with the k‐out‐of‐n redundancy arrangement under uncertainties

Abstract

A safety instrumented system (SIS) is extensively used to prevent or reduce risk. The Probability of Failure to perform its intended functions on Demand (PFD) of a practical SIS may vary within multiple safety integrity levels (SIL) due to uncertainties relevant to input parameters. An SIS will be considered to be unsafe when its PFD is greater than a prescribed value, and unsafety probability (UP) is employed to measure the unsafety degree of the investigated SIS in this work. Redundancy architecture is commonly employed to improve the reliability of an SIS. This paper investigates the effects of multiple uncertain input parameters on the UP of an SIS with the k‐out‐of‐n redundancy arrangement. We derive the detailed formulations of the sensitivity for such effects and we also discuss the physical meaning of the proposed sensitivity. An example is employed to demonstrate the proposed sensitivity and the results show that the estimated sensitivity values will be kept to be unchanged with respect to the redundancy when the redundancy is high, whereas the results will vary with the redundancy when the redundancy is low. Meanwhile, we provide a comparison of the results for the truncated uncertain parameters and the non‐truncated uncertain parameters. The results for truncated uncertain parameters and non‐truncated uncertain parameters will approach the same values as the truncated region of the uncertain parameter reduces to zero. The results show that we can approximate the sensitivities of the truncated parameters by the ones of the non‐truncated parameters with less computation time when the truncated region is less than 10−3.

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