An experimental comparison of linear regression methods used in multi-response design parameter optimization for their estimation and prediction errors

Thesis Type: Postgraduate

Institution Of The Thesis: Orta Doğu Teknik Üniversitesi, Faculty of Engineering, Department of Industrial Engineering, Turkey

Approval Date: 2016




Product and process designers need to find most preferable settings of design parameters to simultaneously achieve multiple quality objectives based on some performance measures such as means and variances of quality characteristics. In these optimization studies, typically empirical models of such performance measures are utilized. These models are usually developed based on data collected through statistically designed experiments using linear regression methods such as Ordinary Least Squares (OLS), Weighted Least Squares (WLS), and Seemingly Unrelated Regression (SUR). In multi-response design parameter optimization (MRDPO) problems, it is assumed that each response has a non-homogeneous variance. Furthermore, responses might be correlated. These linear regression methods might not be appropriate for a particular MRDPO problem due to their restrictive assumptions. Hence, estimation errors associated with model parameters and prediction errors associated with individual observations might be large depending on the problem situation. In this study, we are interested in examining and comparing these errors on a typical MRDPO problem with two responses under different scenarios systematically generated by statistical design of experiments. In addition, we develop a bootstrapping approach to compute joint confidence and prediction regions for estimated mean responses and individual observations, respectively, since these regions are not analytically available for some methods. Our observations based on analysis of experimental results using certain performance measures and graphs of the confidence and prediction regions are presented. Concluding remarks are given and future studies are recommended for generalization of these observations.