A Confidence Region for Optimal Factor Levels Subject to a Constrained Region
A Confidence Region for Optimal Factor Levels Subject to a Constrained Region
John J. Peterson
Abstract: For a response surface experiment, an approximate hypothesis test and an associated confidence region is proposed for the minimizing (or maximizing) factor-level configuration within a specified, bounded region. These constraint regions can be quite general. This allows for more realistic constraint modeling and a wide degree of applicability including constraints occurring in mixture experiments. The usual assumption of a quadratic model is also generalized to include any regression model that is linear in the model parameters. An intimate connection is established between this confidence region and the Box-Hunter (1954) confidence region for a stationary point (in an unconstrained setting). As a byproduct this methodology also provides a way to construct a confidence interval for the difference between the optimal mean response and the mean response at a specified factor level configuration . The application of this confidence region is illustrated with three examples. Some related simulations indicate that this confidence region has good coverage properties.
