Sequem: Estimating extreme steady-state quantiles via the maximum transformation

This article presents Sequem, a fully sequential procedure for computing point estimators and confidence intervals (CIs) for extreme steady-state quantiles of a simulation output process. The method is an enhancement of the Sequest procedure proposed by Alexopoulos et al. in 2014 for estimating nonextreme steady-state quantiles. Sequem exploits a combination of batching, sectioning, and the maximum transformation technique to achieve the following: (a) reduction in point-estimator bias arising from initial conditions or inadequate simulation run length; and (b) adjustment of the CI half-length to compensate for the effects of skewness or correlation in the corresponding quantile point estimators obtained from nonoverlapping batches. The CIs delivered by Sequem satisfy user-specified requirements related to coverage probability and absolute or relative precision. A preliminary evaluation based on three “stress-testing” processes revealed that Sequem exhibited good performance when used in challenging settings.