摘要

It is an elementary fact that the size of an orthogonal array of strength t on k factors must be a multiple of a certain number, say L-t, that depends on the orders of the factors. Thus L-t is a lower bound on the size of arrays of strength t on those factors, and is no larger than L-k, the size of the complete factorial design. We investigate the relationship between the numbers L-t, and two questions in particular: For what t is L-t < L-k? And when L-t = L-k, is the complete factorial design the only array of that size and strength t? Arrays are assumed to be mixed-level.We refer to an array of size less than L-k as a proper fraction. Guided by our main result, we construct a variety of mixed-level proper fractions of strength k - 1 that also satisfy a certain group-theoretic condition.

  • 出版日期2017

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