Experimental Design and Avoiding Confounding Among Estimates of Any Given Set of Effects or Interactions

In k 2 experimental design, the classical fractional factorial designs, the Plackett-Burman designs and the Taguchi orthogonal-array designs all require, with few exceptions, n 2 test conditions, for some k n ≤ . Tsao and Wibowo (2005) pointed out that when only m of the k 2 effects/interactions are non-zero, only m test conditions are required for their estimation. Given the identities of m presumed non-zero effects/interactions, they developed a method to identify a set of exactly m test conditions. Confounding is a major issue for use of any non-full factorial design. The concept of resolution has been developed as a way to describe qualitatively the worst level of confounding. Building on the work of Tsao and Wibowo, this paper focuses on the issue of confounding and shows that their method can be used to avoid confounding among any given set of effects/interactions and to achieve any desired resolution level.