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Maximum and Minimum Prediction Variance for Spherical and Cuboidal Split Plot Designs |
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| Authors: | Wayne R. Wesley James R. Simpson Peter A. Parker Joseph J. Pignatiello Jr. |
| Affiliation: | 1. School of Engineering , University of Technology, Jamaica , Kingston, Jamaica wwesley@ utech.edu.jm or wwesley3@hotmail.com;3. Department of Industrial and Manufacturing Engineering , Florida State University , Tallahassee, Florida, USA;4. Systems Engineering Directorate , NASA Langley Research Center , Hampton, Virginia, USA |
| Abstract: | The impact of restricted randomization on the information matrix has created challenges for the computation of design optimality criteria. This article focuses on the computation of the maximum and minimum prediction variance for Central Composite (CCD) and Box–Behnken (BBD) split plot designs (SPD). The approach is to analytically determine the exact maximum and minimum prediction variance for both spherical and cuboidal second-order SPD. A particular feature of these analytical functions is that they are functions of the design parameters. Finally, the application of these analytical functions is demonstrated for a CCD SPD. |
| Keywords: | Design optimality Prediction variance Restricted randomization Response surface designs Split-plot designs |