Optimization for rising or falling ridge systems in non-spherical designs

Abstract

The response surface (RS) methodology is a well-known tool employed for product and process optimization. In some engineering optimization problems the fitted response has a rising or falling ridge system, namely the stationary point of response is remote from the design region. For such a case, usually the classical method, called ridge analysis (RA), is employed to specify the optimum operating conditions for an optimization problem. In this paper, it is proven that the RA does not guarantee the global maximum or minimum point of response in the experimental region for non-spherical designs such as face-centered designs, Box-Behnken designs, and two-level factorial designs. The current study proposes an approximation based on the use of desirability function technique to solve this ridge optimization problem, and demonstrates that the desirability function technique is more effective than the RA technique described by Myers and Montgomery (2002) for non-spherical designs which are frequently applied for engineering problems. To show the effectiveness and advantages of the proposed technique, a case study is presented to optimize the forming parameters of a tube hydroforming (THF) process where a Box-Behnken design is employed.