Response Surfaces for the Mean and Variance Using a Nonparametric Approach

Engineers and statisticians must consider both the expected value and the process variance when specifying appropriate operating conditions for an industrial process. One approach estimates separate models for the response and for the process variance. In many cases, ordinary least squares does not produce a very good fit to the process variance data. This paper investigates the use of nonparametric regression to estimate the process variance. The response function is then estimated in two ways: (1) using a weighted least squares framework, and (2) using another nonparametric regression for the response. An example illustrates how these methodologies can be used to suggest optimal operating conditions.