Gg. Vining et Ll. Bohn, RESPONSE SURFACES FOR THE MEAN AND VARIANCE USING A NONPARAMETRIC APPROACH, Journal of quality technology, 30(3), 1998, pp. 282-291
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 lea
st squares does not produce a very good fit to the process variance da
ta. This paper investigates the use of nonparametric regression to est
imate 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 illustr
ates how these methodologies can be used to suggest optimal operating
conditions.