Estimating the Error in LHS Predictions

Abstract

The convergence properties for Latin Hypercube Sampling (LHS) for reliability analyses is studied and compared with Simple Random Sampling (SRS) which has relatively wellknown error estimates. This paper summarizes the anticipated error of LHS estimates for percentile statistics of the response. For the relatively simple case, LHS yields dramatic improvements where the variance of the estimate is 1/N times that of SRS. However, for cases with many important variables, the improvement is diminished and often tends to a constant such as 1/3. In no case is the performance of LHS worse that SRS, so that one can expect LHS to continue to be a popular alternative to SRS when a direct sampling method is needed. Nomenclature fx = joint density function g = limit state function n = number of samples pf = probability of failure x = input variable(s) Z = response function