Construction of \(2^ m4^ n\) designs via a grouping scheme. (English) Zbl 0695.62198

Wu, C. F. J.

Ann. Stat. 17, No. 4, 1880-1885 (1989).

Summary: We develop a method for grouping the \(2^ k-1\) factorial effects in a 2- level factorial design into mutually exclusive sets of the form (s,t,st), where st is the generalized interaction of effects s and t. As an application, we construct orthogonal arrays \(OA(2^ k,2^ m4^ n,2)\) of size \(2^ k\), m constraints with 2 levels and n constraints with 4 levels satisfying \(m+3n=2^ k-1\), and strength 2. The maximum number of constraints with 4 levels in the construction cannot be further improved. In this sense our grouping scheme is optimal. We discuss the advantage of the present approach over other construction methods.

MSC:

62K15	Factorial statistical designs
05B15	Orthogonal arrays, Latin squares, Room squares

Keywords:

fractional factorial designs; method of replacement; symmetric difference; optimal grouping; factorial effects; generalized interaction of effects; orthogonal arrays; maximum number of constraints; grouping scheme