Type 1 optimal [formula omitted] fractional factorial plans with [formula omitted] (mod 8) runs, [formula omitted

Abstract

This paper considers the issue of optimality of fractional factorial experiments involving m factors each at two levels. The optimality criteria used here is the type 1 criteria, due to Cheng (1978), which include the D - and A -criteria. It is shown that if there exists an orthogonal array O A ( n − ℓ , m , 2 , 3 ) , ℓ = 1 , 2 , then there exists an n -run type 1 optimal fractional factorial plan for a 2 m experiment under a model that includes the mean, all main effects and all two-factor interactions with a factor in common. These plans are obtained by adding any one run to an O A ( n − 1 , m , 2 , 3 ) for n ≡ 1 (mod 8) and two specific runs to an O A ( n − 2 , m , 2 , 3 ) for n ≡ 2 (mod 8).