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Classical Design Generators for Non-Regular Designs Arising from the Custom Design Platform

Mark Johnson, PhD, Professor of Statistics, University of Central Florida
Seiichi Yasui, PhD, Assistant Professor, Tokyo University of Science

JMP Pro 11 facilitates the generation of fractional factorial designs having desirable properties via Custom Design and the new Definitive Screening Design platforms. Jones and Montgomery (2010) provided a very compelling example of one particular Custom Design in which the correct main effects and the active two-way interaction were identified while avoiding a follow-up experiment. On first encounter, this example seems miraculous, but within this design lurks potentially annoying multicollinearities involving pairs of main effects with pairs of two-way interactions. It is as if one issue (additional runs) has been inadvertently exchanged for another one, albeit less onerous (multicollinearities). Partial confounding of additional factors with main effects is also a feature occurring in the screening designs having minimal aliasing developed by Jones and Nachtsheim (2011). Characterizing the underlying generating relations associated with 16 run, 6/7/8 factor custom designs was accomplished by Johnson and Jones (2011), although admittedly some of these designs look rather quirky. Since the designs produced by Custom Design and the Definitive Screening Design are increasingly being used, we have been striving to make sense of the associated generating relations. Ultimately, these results further bridge the gap between the classical and the D-optimal paradigms of experimental design.

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