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Split-plot designs for multistage experimentation

机译：用于多阶段实验的分割图设计

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摘要

Most of today's complex systems and processes involve several stages through which input or the raw material has to go before the final product is obtained. Also in many cases factors at different stages interact. Therefore, a holistic approach for experimentation that considers all stages at the same time will be more efficient. However, there have been only a few attempts in the literature to provide an adequate and easy-to-use approach for this problem. In this paper, we present a novel methodology for constructing two-level split-plot and multistage experiments. The methodology is based on the Kronecker product representation of orthogonal designs and can be used for any number of stages, for various numbers of subplots and for different number of subplots for each stage. The procedure is demonstrated on both regular and nonregular designs and provides the maximum number of factors that can be accommodated in each stage. Furthermore, split-plot designs for multistage experiments with good projective properties are also provided.
机译：当今大多数复杂的系统和过程都涉及多个阶段，在这些阶段中，必须先投入投入或原材料，然后才能获得最终产品。同样，在许多情况下，处于不同阶段的因素也会相互作用。因此，同时考虑所有阶段的整体实验方法将更加有效。但是，在文献中只有很少的尝试为该问题提供适当且易于使用的方法。在本文中，我们提出了一种用于构造两级分裂图和多阶段实验的新颖方法。该方法基于正交设计的Kronecker产品表示，可用于任何数量的阶段，不同数量的子图以及每个阶段的不同数量的子图。该程序在常规和非常规设计中都得到了证明，并提供了每个阶段可以容纳的最大因素数。此外，还提供了具有良好投射特性的用于多阶段实验的分割图设计。

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