Effect of Truncated Input Parameter Distribution on the Integrity of Safety Instrumented Systems Under Epistemic Uncertainty

Abstract

Safety instrumented system (SIS) is widely applied to reduce or prevent risk in industry. Practical SIS commonly meets with epistemic uncertainty arising from incompleteness of knowledge on various input parameters due to lack of data. Epistemic uncertainty can be reduced by collecting more knowledge or data. Epistemic uncertainty in input parameters can lead to variation in probability of failure to perform its intended functions on demand (PFD) for an SIS. This paper employs the complementary cumulative distribution function of PFD to define exceedance probability (EP) that the PFD exceeds a prescribed value. Sensitivity analysis is further investigated, analyzing the effect of an epistemically uncertain input parameter with truncated distribution on EP of an SIS. We have derived the analytic expression for evaluating the effect, and only an evaluation is needed to estimate the effects of all the parameters. Two examples are employed to demonstrate the applicability of the proposed method. We further compare the effects for the truncated and nontruncated parameter situations. Their results converge to the same ones as the truncated region of an input parameter decreases to zero. When the truncated region of an input parameter is less than 10-3, the corresponding results can be approximated by the ones of the nontruncated case with lower computational cost.

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