Dual Response Surface Optimization based on Skill Scores

Abstract

The popular formulations of dual-response optimization are constructed on minimizing a function of bias and system variability. This study provides an opportunity to evaluate the dual response surface (DRS) problem from a different perspective by adapting two new terms such that internal and external quality forecasts. The background of the proposed approach focuses on the relationship between internal and external quality forecasts and discusses the DRS problem in regards of skill scores by defining a model quality criterion. Skill is the relative accuracy of the forecast and defines a correspondence between forecast of interest and reference forecasts. The reference forecast does not require any knowledge or modelling; thus, it is an unskilled forecast. In this context, skill score is a measure of this relative improvement and widely used in evaluating the performance of operational and experimental forecasts. An alternative version of mean square error (MSE) which is reconstructed by skill scores and model quality criterion is proposed as an objective function for the DRS problem. Integrating the relationship between internal and external quality forecasts into such a response function can improve the effectiveness and cooperation of the applied technique. The proposed approach has a flexible structure and provides decision makers alternative solutions for different values of the model quality criterion. The proposed procedure is discussed by conducted a simulation study and demonstrated in an engineering process.