Model-based approaches for robust parameter design

Since Taguchi methods have been introduced in many major American industries, quality improvement experiments have emphasized optimizing the mean value of the performance characteristics, while placing secondary attention on the variance. However, some weaknesses in Taguchi methods have been identified, and some controversies still exist. As an alternative, several researchers have combined important aspects of the Taguchi methods with classical response surface methods. The focus in these enhancements has been placed on building models that involve direct interactions between the control factors (CxC), and establishing separate models for the mean and variance of the performance characteristics. In this paper, the responses of the mean and variance are derived according to the following scenarios: i) a model with control and external noise factors, ii) a model with control and internal noise factors, and iii) a model with control, external noise, and internal noise factors. Also, both the mean and variance can be obtained using combined and product arrays. Particularly, the model used is represented by linear main effects in the control and noise (N) factors, two-factor interactions and quadratic terms in the control factors, second-order CxN interactions, and possibly some third-order CxCxN interactions, even though these third-order interactions may be less important than the first-order or second-order effects. In addition, these third-order terms should be included in modeling the performance characteristics when the product array is used for the experiments.