Quantifying LOPA uncertainty

Abstract

Layer of protection analysis (LOPA) is a semi‐quantitative risk evaluation tool. The methodology is widely used in setting safety integrity level (SIL) targets for safety instrumented systems (SIS). The methodology is often used to evaluate the adequacy of existing protective systems against corporate risk targets. The LOPA method is based on the use of conservative but representative estimates of the failure probability of protective systems. The results of these studies are presented to management for concurrence with the conclusions and for funding of recommendations. Management sometimes asks questions such as: What is the uncertainty in the results? How sensitive are the results to the underlying data and assumptions? How conservative is the LOPA methodology? Should additional independent protection layers be recommended from the LOPA study to compensate for uncertainty in the results? There is no existing method for the analysis of uncertainty in a LOPA study. This article presents a framework to answer management questions related to the LOPA uncertainty. Guidance is presented on methods to incorporate an uncertainty analysis into a LOPA or quantitative risk analysis study. © 2012 American Institute of Chemical Engineers Process Saf Prog, 2012

Simplified uncertainty analysis of layer of protection analysis results

“…With these estimates for the partial derivatives, the variance contribution from each of the uncertain random variables may now be computed (see Table ). Note that the results in Table are identical with those previously obtained by Freeman using more formal mathematical methods. The same result could be obtained by simple numerical substitution.…”

“…Since the variance contribution and total variance are the same whether computed via an analytical method or by a numerical approximation method, the accuracy of the resulting will be the same as previously reported by Freeman . Table presents a comparison of the computed results with those previously obtained by Freeman using both an analytical and a Monte Carlo method for estimating the frequency of overpressure of the Hold Drum in the example problem.…”

“…Using VCA, the mean, and variance for the LOPA equation are found directly per the work of Freeman . For the expression: where Y = dependent random variable computed from x i , F ( x i ) = function that converts (maps) random variable x i into Y .…”

“…Previously, Freeman presented an example problem to demonstrate the direct application of VCA to the uncertainty in the LOPA calculations. The same example is used for comparison in this work.…”

“…Freeman developed a method for evaluating the uncertainty in a LOPA study using a mathematical method called variance contribution analysis (VCA). The VCA method outlined in Freeman's article requires the evaluation of the partial derivative of the basic LOPA equation for each of the uncertain variables.…”