Bayesian-inspired minimum contamination designs under a double-pair conditional effect model

In two-level fractional factorial designs, conditional main effects can provide insights by which to analyze and facilitate the de-aliasing of fully aliased two-factor interactions. Conditional are particular interest in situations where some factors nested within others. Most relevant literature has focussed on development data analysis tools that use effects, while issue optimal design for a given linear model involving been largely overlooked. Mukerjee, Wu Chang [Statist. Sinica 27 (2017) 997–1016] established framework optimize designs under effect model. Although theoretically sound, their results were limited single pair conditioning factors. this paper, we extend applicability double pairs providing corresponding parameterization hierarchy. We propose minimum contamination-based criterion evaluate develop complementary set theory search contamination designs. The catalogues 16- 32-run provided. For five twelve factors, show all 16-run also aberration according Fries Hunter [Technometrics 22 (1980) 601–608].