An Optimal Split-Plot Design for Performing a Mixture-Process Experiment

G. Njoroge, J. Simbauni, J. Koske
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引用次数: 5

Abstract

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 2 2 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.
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混合工艺实验的最优分割图设计
在许多混合工艺实验中,发生了有限的随机化,通常采用分裂图设计来处理这些情况。本研究的目的是获得进行混合工艺实验的最佳分割图设计。采用三种混合成分的单纯形质心设计和工艺因素的22因子设计相结合的分裂图设计。比较了分块设计中设计点的两种不同安排。Design-Expert®version 10软件用于构建i和d最优分割图设计。本研究采用A-、D-和E-最优性标准来比较构建设计的效率,并使用设计空间图的分数来评估两种设计的预测特性。发现子图多于整体图的排列更有效,并且根据A-, D-和e-最优性标准给出更精确的参数估计。由于i -最优分割图设计在系数测量中具有更好的预测性能和精度,因此优选该设计。因此,我们建议在涉及混合配方的实验中采用分裂图设计来测量混合成分和加工条件的相互作用效应。在混合结果的精度更理想的情况下,以及混合混合超过工艺条件集的情况下,我们建议在析因设计的每个点上设置混合实验。在对系统的预测方面感兴趣的情况下,我们建议采用i -最优分割图设计,因为它在大部分设计空间中具有较低的预测方差,并且还提供了相当精确的参数估计。
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