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Large factorial designs for product engineering and marketing research applications

机译：适用于产品工程和市场研究应用的大型析因设计

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Engineers and marketing researchers working on optimal product design share many design requirements. Orthogonal arrays and factorial designs are commonly used. Orthogonality and balance are important, but not only for reasons of statistical efficiency. Balance (or near balance) helps ensure that the product sets will be perceived as unbiased by clients, managers, and the human subjects to whom they are presented. Small D-efficient factorial designs can be found by searching the full-factorial candidate set using a modified Fedorov (Mfed) algorithm (Refs. 1,2), building an initial design from the candidate runs, and considering exchanging each candidate/design pair. Exchanges that increase D-efficiency are performed. D-efficiency is a function of the determinant of the design's information matrix, typically scaled relative to the same function from a (perhaps hypothetical) balanced and orthogonal design and expressed in percentage units: D-efficiency = 100/(n | X'X)~(-1) |~(l/p)) for n runs, p parameters, and design matrix X. Here X is orthogonally coded so that a balanced and orthogonal design has 100 percent D-efficiency. Each Mfed search has run time approximately proportional to the number of candidate points, making Mfed impractical for large candidate sets. When the full-factorial is too large to search with Mfed (which is usually the case for marketing research designs), researchers instead search a suitably fractionated candidate set. With the right candidate set, this approach works quite well. However, creating a suitable candidate set can be difficult, even with the aid of sophisticated search tools such as the SAS procedure FACTEX (Ref. 3).
机译：致力于最佳产品设计的工程师和市场研究人员共享许多设计要求。通常使用正交阵列和阶乘设计。正交和平衡很重要，但不仅是出于统计效率的原因。平衡（或接近平衡）有助于确保客户，经理和所展示的对象不会偏向于产品集。通过使用改良的Fedorov（Mfed）算法（参考1,2）搜索全因子候选集，从候选运行中构建初始设计，并考虑交换每个候选/设计对，可以找到小型的D有效阶乘设计。 。进行提高D效率的交换。 D效率是设计信息矩阵行列式的函数，通常相对于（可能是假设的）平衡和正交设计中相对于同一函数进行缩放，并以百分比单位表示：D效率= 100 /（n | X'X ）〜（-1）|〜（l / p））对于n个行程，p个参数和设计矩阵X。这里X是正交编码的，因此平衡且正交的设计具有100％的D效率。每个Mfed搜索的运行时间大约与候选点的数量成正比，因此对于大型候选集而言，Mfed不切实际。当全因数太大而无法使用Mfed进行搜索时（营销研究设计通常是这种情况），研究人员会搜索适当细分的候选集。选择合适的候选人，这种方法效果很好。但是，即使借助诸如SAS程序FACTEX（参考文献3）之类的复杂搜索工具，也很难创建合适的候选集。

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