A-OPTIMAL BALANCED FRACTIONAL 2_m FACTORIAL DESIGNS OF RESOLUTION V WITH TWO BLOCKS, 4≤m≤6

Abstract

Consider a balanced fractional 2_m factorial design of resolution V with two blocks derived from a balanced array (B-array) of strength 4. Furthermore, it is constructed by two subarrays with N₁ and N₂ assemblies (or treatment combinations), which are B-arrays of strength 2 and correspond to two blocks. In this paper, we present A-optimal designs with N (=N₁+N₂) assemblies for the following two cases: One is the case where N₂=N₁ if N is even and N₂=N₁+1 if N is odd, and N_k≤v(m), where v(m) is the number of the main effects and the two-factor interactions in the model assumed, i.e., v(m)=m+(_m²). The other is the case where v(m)≤N≤2v(m) and 1≤N_k≤v(m).
AMS 1980 subject classifications: Primary 62K05, Secondary 62K15.