(44au) Simplified Uncertainty Analysis of LOPA Results

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. 

 Previously Freeman has 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.  While mathematically correct, this use of a partial derivative analysis during an actual LOPA review is unlikely.  Faster and easier methods are needed if LOPA uncertainty analysis is to be applied by practicing engineers.

 This paper 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%. When evaluating simple safety systems designed per IEC 61511, the error is found to be no more than 10% for SIL-1 or SIL-2 capable systems.  When compared to direct Monte Carlo simulation methods, the numerical approximation method is much more efficient.  Monte Carlo simulation takes approximately 10,000 function evaluations to arrive at a result.  For the base line problem studied, the approximate method will take only 5 function evaluations.

 Using the results of the simplified methods, guidance is presented on methods to incorporate an uncertainty analysis into a LOPA study to establish SIL target design levels.  A set of data Tables for use during the LOPA uncertainty analysis are develoeped for initiating events and independent protection layers (IPLs).