A Robust Multi Response Surface Approach for Optimization of Multistage Processes

Purpose: In a multistage process, the final quality in the last stage not only depends on the quality of the task performed in that stage but also is dependent on the quality of the products and services in intermediate stages as well as the design parameters in each stage. One of the most efficient statistical approaches used to model the multistage problems is the response surface method (RSM). However, it is necessary to optimize each response in all stages so to achieve the best solution for the whole problem. Robust optimization can produce very accurate solutions in this case.

Design/methodology/approach: In order to model a multistage problem, the RSM is often used by the researchers. A classical approach to estimate response surfaces is the ordinary least squares (OLS) method. However, this method is very sensitive to outliers. To overcome this drawback, some robust estimation methods have been presented in the literature. In optimization phase, the global criterion (GC) method is used to optimize the response surfaces estimated by the robust approach in a multistage problem.

Findings: The results of a numerical study show that our proposed robust optimization approach, considering both the sum of square error (SSE) index in model estimation and also global criterion (GC) index in optimization phase, will perform better than the classical full information maximum likelihood (FIML) estimation method.

Originality/value: To the best of the authors’ knowledge, there are few papers focusing on quality oriented designs in the multistage problem by means of RSM. Development of robust approaches for the response surface estimation and also optimization of the estimated response surfaces are the main novelties in this study. The proposed approach will produce more robust and accurate solutions for multistage problems rather than classical approaches.