Optimal sequencing of test conditions in 2k factorial experimental design for run-size minimization

The exponential growth of the number of test conditions (i.e., the “run size”) of a 2k factorial design makes the design prohibitively expensive for a large k. When only m of the 2k effects/interactions are non-zero, only m test conditions are required for their estimation. However, both fractional factorial design and Taguchi method require 2n test conditions, for some n ⩽ k, and therefore may require more test conditions than necessary. Given the identities of the m non-zero effects/interactions, Tsao and Wibowo recently developed an algorithm to identify a set of exactly m test conditions but did not suggest how to test the adequacy of the m-unknown model or how to expand the set of test conditions incrementally when more non-zero effects/interactions actually exist.This paper proposes to incrementally and efficiently expand the model by developing an effect–interaction sequence in the descending order of their magnitudes. Given any such sequence, we provide a simple algorithm to sequence the 2k test conditions so that, for any m, 1 ⩽ m ⩽ 2k, the first m effects/interactions in the effect–interaction sequence can be estimated with exactly the first m test conditions in the corresponding test-condition sequence and no more, if all the other 2k − m effects/interactions are zero. A benefit of this is that experiments can be performed sequentially according to the test-condition sequence until the first insignificant effect/interaction is found. The proposed method can also be used for situations where knowledge about the effects/interactions is too vague to sort them according to their magnitudes.