A split-plot experiment with factor-dependent whole-plot sizes
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.
To reference this document use:
QS - Quality & Safety
EELS - Earth, Environmental and Life Sciences
Journal of Quality Technology, 43 (1), 66-79