Prediction variance of a central composite design with missing observation

Abstract

Central composite design has been widely used in response surface methods. This article studies how much the variance of a predicted response is inflated when an observation is missing in a central composite design. A mathematical expression is derived for the inflation amount of the prediction variance. It turns out that, for rotatable central composite designs, the inflation amount of the prediction variance depends only on the Euclidean norms and the inner product of the two vectors of factor values at which the observation is missing and the response is predicted. Several numerical examples are presented to show relationships between the inflation amount of the prediction variance and the angle formed by the two vectors.

Keywords:

• Central composite design
• missing data
• prediction variance
• response surface method
• rotatable design

Acknowledgments

The authors would like to thank anonymous reviewers for constructive comments.

Additional information

Funding

This work was supported by Japan Society for the Promotion of Science KAKENHI Grant Number 15K15952.