工业工程2012，Vol.15Issue(3)：98-103,6.DOI:10.3969/j.issn.1007-7375.2012.03.019
响应曲面建模的稳健M-回归方法
The robust M-estimators in Response Surface Modeling
摘要
Abstract
Response surface methodology is a powerful tool for product/process improvement and optimization. In response surface modeling, the random errors are assumed to be normally distributed independent random variables with constant variance. However, due to the fact that outliers are inevitable in the observations , the constant variance assumption does not hold in practice. To dampen the effect of such observation random errors on the least square regression model, robust regression techniques are employed. Consider that the outlier which may occur in different experimental region and based on central composite design , performance analysis of reducing the influence of outliers for the M-estimators of robust regression is made. It includes three estimators; Huber-estimator, Tukey-estimator, and Welsch-estimator. By comparison, it shows that Welsch and Tukey-estimators are better than Huber-estimator in reducing the effect of outliers among response surface optimization and in response surface design. An example from chemical industry is used to calculate the optimal value of response surface model based on different experiment region of central composite design with and without outlier. In other words, the robust M-estimators, especially Welsch and Tukey-estimators, significantly improve the robustness of response surface modeling in large magnitude outliers (10 standard deviation).关键词
响应曲面/稳健M-回归/中心复合设计Key words
response surface methodology/ robust M-estimators/ central composite design分类
管理科学引用本文复制引用
方俊涛,何桢,宋琳曦,张阳..响应曲面建模的稳健M-回归方法[J].工业工程,2012,15(3):98-103,6.基金项目
国家自然科学基金重点资助项目(70931004) （70931004）
国家自然科学基金面上项目(70871087) （70871087）
