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Simplified uncertainty analysis of layer of protection analysis results

Layer of protection analysis (LOPA) is a semiquantitative risk evaluation tool. The methodology is widely used in setting safety integrity level targets for safety instrumented systems. 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 estimates of the failure probability of protective systems. Freeman previously presented a method for the quantification of uncertainty in a LOPA study based on the application of variance contribution analysis (VCA) techniques. The use of VCA to evaluate the uncertainty in a LOPA study requires the evaluation of the sensitivity of the LOPA equation to changes in each of the variables. Freeman used direct analytical computation of the partial derivatives of the LOPA equation for each of the uncertain variables. Faster and easier methods are needed if LOPA uncertainty analysis is to be applied by practicing engineers. This article explores the use of approximations to compute the required uncertainty information without the use of the partial derivative computations. Numerical approximations (perturbation methods) are found to allow for the estimate of the partial derivatives with a maximum error of 16%. © 2013 American Institute of Chemical Engineers Process Saf Prog 32: 351–360, 2013