Construction of two-level irregular minimum aberration fractional factorial plans

Abstract

Irregular two-level fractional factorial designs are the plans that can not be specified in terms of defining contrasts. The aliasing properties of irregular fractional factorial plans can be explained by using minimum moment aberration and moment aberration projection criterion. In this paper a method of construction for irregular minimum aberration fractional factorial designs of the type $\frac{\mathit{r}}{2^{\mathit{p}}}\mathrm{(}{2}^{\mathit{k}}\mathrm{)}$ , where r is a prime number has been given. Also minimum aberration designs have been constructed for $\mathit{r}=3$ , $\mathit{p}=2$ and $\mathit{k}=4\mathrm{,}5\mathrm{,}6\mathrm{,}7$ ; for $\mathit{r}=3$ , $\mathit{p}=3$ and $\mathit{k}=5\mathrm{,}6\mathrm{,}7\mathrm{,}8$ ; for $\mathit{r}=5$ , $\mathit{p}=3$ and $\mathit{k}=5\mathrm{,}6\mathrm{,}7\mathrm{,}8$ and $\mathit{r}=7$ , $\mathit{p}=3$ and $\mathit{k}=5\mathrm{,}6\mathrm{,}7\mathrm{,}8$ by using the two criteria, viz. minimum moment aberration and moment aberration projection.