Model selection and analysis tools in response surface modeling of the process mean and variance
Product improvement is a serious issue facing industry today. And while response surface methods have been developed which address the process mean involved in improving the product there has been little research done on the process variability. Lack of quality in a product can be attributed to its inconsistency in performance thereby highlighting the need for a methodology which addresses process variability. The key to working with the process variability comes in the handling of the two types of factors which make up the product design: control and noise factors. Control factors can be fixed in both the lab setting and the real application. However, while the noise factors can be fixed in the lab setting, they are assumed to be random in the real application. A response-model can be created which models the response as a function of both the control and noise factors. This work introduces criteria for selecting an appropriate response-model which can be used to create accurate models for both the process mean and process variability. These two models can then be used to identify settings of the control factors which minimize process variability while maintaining an acceptable process mean.
If the response-model is known, or at least well estimated, response surface methods can be extended to building various confidence regions related to the process variance. Among these are a confidence region on the location of minimum process variance and a confidence region on the ratio of the process variance to the error variance. It is easy to see the importance for research on the process variability and this work offers practical methods for improving the design of a product.