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An Optimal Split-Plot Design for Performing a Mixture-Process Experiment
Science Journal of Applied Mathematics and Statistics
Volume 5, Issue 1, February 2017, Pages: 15-23
Received: Oct. 30, 2016; Accepted: Nov. 21, 2016; Published: Jan. 18, 2017
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Gladys Gakenia Njoroge, Department of Physical Sciences, Chuka University, Chuka, Kenya
Jemimah Ayuma Simbauni, Department of Zoological Sciences, Kenyatta University, Nairobi, Kenya
Joseph Arap Koske, Department of Mathematics and Computer Science, Moi University, Eldoret, Kenya
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In many mixture-process experiments, restricted randomization occurs and split-plot designs are commonly employed to handle these situations. The objective of this study was to obtain an optimal split-plot design for performing a mixture-process experiment. A split-plot design composed of a combination of a simplex centroid design of three mixture components and a 22 factorial design for the process factors was assumed. Two alternative arrangements of design points in a split-plot design were compared. Design-Expert® version 10 software was used to construct I-and D-optimal split-plot designs. This study employed A-, D-, and E- optimality criteria to compare the efficiency of the constructed designs and fraction of design space plots were used to evaluate the prediction properties of the two designs. The arrangement, where there were more subplots than whole-plots was found to be more efficient and to give more precise parameter estimates in terms of A-, D- and E-optimality criteria. The I-optimal split-plot design was preferred since it had the capacity for better prediction properties and precision in the measurement of the coefficients. We thus recommend the employment of split-plot designs in experiments involving mixture formulations to measure the interaction effects of both the mixture components and the processing conditions. In cases where precision of the results is more desirable on the mixtures as well as where the mixture blends are more than the sets of process conditions, we recommend that the mixture experiment be set up at each of the points of a factorial design. In situations where the interest is on prediction aspects of the system, we recommend the I-optimal split-plot design to be employed since it has low prediction variance in much of the design space and also gives reasonably precise parameter estimates.
Optimality, Split-Plot Design, Efficiency, Mixture Components, Process Variables
To cite this article
Gladys Gakenia Njoroge, Jemimah Ayuma Simbauni, Joseph Arap Koske, An Optimal Split-Plot Design for Performing a Mixture-Process Experiment, Science Journal of Applied Mathematics and Statistics. Vol. 5, No. 1, 2017, pp. 15-23. doi: 10.11648/j.sjams.20170501.13
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This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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