Sensitivity Analysis Using the Monte Carlo Acceptance-Rejection Method

This paper describes a Monte Carlo sampling plan for estimating how a function varies in response to changes in its arguments. Most notably, the plan effects this sensitivity analysis by applying the acceptance-rejection technique to data sampled at only one specified setting for the arguments, thus saving considerable computing time when compared to alternative methods. The plan which applies for a 0-1 response on each replication has immediate application when estimating variation in system performance measures in reliability analysis. The paper derives the variances of the proposed estimators and shows how to use worst case bounds on these or on corresponding coefficients of variation to choose the arguments, at which to sample, that minimize the worst case bounds. Individual and simultaneous confidence intervals are derived and an example based on s-t reliability illustrates the method. The paper also compares the proposed method and an alternative Monte Carlo approach that uses an importance function.