Using Monte-Carlo variance reduction in statistical tolerance synthesis

A statistical tolerance synthesis must analyse many sets of tolerances, each of which has a unique probability distribution. The Monte-Carlo technique that is typically used to evaluate the probability distribution must analyse large numbers of individual cases. The result is a huge number of individual analyses, which is computationally expensive. This paper examines two Monte-Carlo variance reduction techniques, importance sampling and correlation, and proposes a method for using them in statistical tolerance synthesis. Correlation is used to reduce the error in the tolerance analyses. Importance sampling is used to estimate the sensitivity of an analysis to the tolerances so that a gradient based optimization algorithm can be used.