Confidence sets for optimal factor levels of a response surface.

Area of Science:

• Statistics
• Experimental Design

Background:

• Confidence sets for optimal factor levels are crucial in response surface methodology.
• Previous work provided exact confidence sets for univariate polynomial functions.

Purpose of the Study:

• To extend the construction of exact (1-α) confidence sets for optimal factor levels in response surfaces.
• To apply the method to parametric and semiparametric regression models with quadratic functions.

Main Methods:

• Extension of existing methods for constructing exact confidence sets.
• Inclusion of a conservative confidence set as an intermediate step.
• Application to regression models involving quadratic functions.

Main Results:

• Development of an exact (1-α) confidence set for optimal factor levels of response surfaces.
• Demonstration of applicability to various regression models.
• Empirical comparison showing superiority over existing methods.

Conclusions:

• The proposed exact confidence set method is a valuable advancement in response surface methodology.
• The method offers improved accuracy and reliability for identifying optimal factor levels.
• This approach provides a better alternative for statistical inference in optimization problems.