A Split-Plot Experiment with Factor-Dependent Whole-Plot Sizes

作者：Schoen Eric^*; Jones Bradley; Goos Peter

来源：Journal of Quality Technology, 2011, 43(1): 66-79.

• Coordinate-Exchange Algorithm
• D-Optimum Designs
• Point-Exchange Algorithm
• Restricted Randomization

Problem: The dairy company FrieslandCampina had an opportunity to redesign the production process for its coffee cream. This product has a very specific viscosity, and the redesigned process had to result in the same viscosity as the old one.
Approach: For an effective redesign, the investigators wanted to obtain a simple model linking the settings of nine controllable factors to the viscosity of the product. They decided to use the results of a statistically designed experiment to build such a model. Two factors were hard to change (HTC) and could only be set six times; the remaining factors were easy to change (ETC). The presence of HTC and ETC factors calls for a split-plot experiment with whole plots defined by the six settings of the HTC factors. However, the number of runs within a whole plot depended on the level of one of the whole-plot factors. Commercial software fails to produce designs for this situation. In this paper, we detail orthogonal and nonorthogonal whole-plot designs for each of three total run sizes and discuss how three existing algorithms to construct optimal split-plot designs can be modified to handle factor-dependent whole-plot sizes.
Results: The experiment was conducted according to one of the designs and viscosity measurements of the products were made. A second-order model, fitted using generalized least squares and restricted maximum likelihood, was used to study the effect of changes to the process design on the viscosity.

• 出版日期2011-1