Robust design for the nominal-the-best performance characteristic

Robust design is an engineering methodology for improving the product quality by minimizing the effect of the causes of variation. For the nominal-the-best robust design problem, Taguchi developed a two-step procedure for identifying the optimal factor/level settings. However, Taguchi's two-step procedure is inefficient in some cases. For instance, it is possible that the mean cannot be shifted to the target when the adjustment factor is qualitative or the adjustment factor can only be adjusted within a limited region. In this case, the procedure may not be able to attain the minimum quality loss even though its SN ratio is maximized. In this work, a simple procedure (Procedure 1) capable of reaching the approximate independence between the sample mean and the sample standard deviation is proposed. Additionally, an efficient procedure (Procedure 2) which will attain the minimum quality loss is also developed. By utilizing stepwise regression and nonlinear programming techniques, Procedure 2 can be used to determine the optimum conditions for the nominal-the-best robust design problems. Moreover, the proposed procedures are compared with Taguchi's two-step procedure through a case study involving the improvement of the wafer quality in the deposition process of the IC fabrication. That comparison reveals that Procedure 2 is the most effective and feasible technique.