Studies on the Effects of Estimator Selection in Robust Parameter Design under Asymmetric Conditions

Abstract

The primary goal of robust parameter design (RPD) is to determine the optimum operating conditions that achieve process performance targets while minimizing variability in the results. To achieve this goal, typical approaches to RPD problems use ordinary least squares methods to obtain response functions for the mean and variance by assuming that the experimental data follow a normal distribution and are relatively free of contaminants or outliers. Consequently, the most common estimators used in the initial tier of estimation are the sample mean and sample variance, as they are very good estimators when these assumptions hold. However, it is often the case that such assumed conditions do not exist in practice; notably, that inherent asymmetry pervades system outputs. If unaccounted for, such conditions can affect results tremendously by causing the quality of the estimates obtained using the sample mean and standard deviation to deteriorate. Focusing on asymmetric conditions, this paper examines several highly efficient estimators as alternatives to the sample mean and standard deviation. We then incorporate these estimators into RPD modeling and optimization approaches to ascertain which estimators tend to yield better solutions when skewness exists. Monte Carlo simulation and numerical studies are used to substantiate and compare the performance of the proposed methods with the traditional approach. Copyright © 2012 John Wiley & Sons, Ltd.