High breakdown estimator for dual response optimization in the presence of outliers

Abstract

Nowadays, dual response surface approach is used extensively, and it is known as one of the powerful tools for robust design. General assumptions are the data is normally distributed, and there is no outlier in the data set. The traditional procedures for robust design is to establish the process location and process scale models of the response variable based on sample mean and sample variance, respectively. Meanwhile, the ordinary least squares (OLS) method is often used to estimate the parameters of the regression response location and scale models. Nevertheless, many statistics practitioners are unaware that these existing procedures are easily influenced by outliers, and hence resulted in less accurate estimated mean response obtained through non-resistant method. As an alternative, the use of MM-location, MM-scale estimator, and MM regression estimator is proposed, in order to overcome the shortcomings of the existing procedures. This study employs a new penalty function optimization scheme to determine the optimum factor settings for robust design variables. The effectiveness of our proposed methods is confirmed by well-known example and Monte Carlo simulations.