Methodological study demonstrates sixteen-run factor screening designs with projectivity three for up to fourteen factors, highlighting enhanced experimental efficiency.
A two level orthogonal array design for n observations with k factors and of projectivity P provides an (n, k, P) factor screen for which every projection into P space produces a complete 2 P factorial, possibly with certain points replicated. Box and Tyssedal [1] Box, G. E.P. and Tyssedal, J. 1996. Projective Properties of Certain Orthogonal Arrays. Biometrika, 83(4): 950–955. [Crossref], [Web of Science ®] , [Google Scholar] rigorously investigated the screening properties of such designs derived from fractional factorials and Plackett Burman orthogonal arrays (OA's). For example, they showed that these always provided (12, 11, 3) and (20, 19, 3) screens, but for 16 runs only a (16, 8, 3) screen could be generated. In this paper it is shown that designs derived from a different class of OA's due to Hall [2] Hall, M. J. 1961. Hadamard Matrices of Order 16 21–26. Jet Propulsion Laboratory. Summary 1 [Google Scholar] can produce sixteen run designs that can screen a larger number of factors and that in particular (16, 12, 3) screens and also a (16, 14, 3) screen can be obtained.
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Box et al. (2001) studied this question.
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