A Note on Discrete Factorial Designs of Resolution Five and Seven and Balanced Arrays

Abstract

In this paper, we consider the use of balanced arrays (B-arrays) in constructing discrete fractional factorial designs (FFD) of resolution $(2u+1)$, with $u=2$ and $3$, in which each of the $m$ factors is at two levels (say, $0$ and $1$), denoted by factorial designs of $2^m$ series. We make use of the well-known fact that such designs can be realized under certain conditions, by using balanced arrays of strength four and six (with two symbols), respectively. Here, we consider the existence of B-arrays of strength $t=4$ and $t=6$, and discuss how the results presented can be used to obtain the maximum value of $m$ for a given set of treatment-combinations. Also, we provide some illustrative examples in which the currently available $max(m)$ values have been improved upon.