Construction of Blocked Factorial Designs to Estimate Main Effects and Selected Two-Factor Interactions

Two-level factorial designs are widely used in industrial experiments. For processes involving $n$ factors, the construction of designs comprising $2^n$ and $2^{n-p}$ factorials, arranged in blocks of size $2^q$ is investigated. The aim is to estimate all main effects and a selected subset of two-factor interactions. Designs constructed according to minimum aberration criteria are shown to not necessarily be the most appropriate designs in this situation. A design construction approach is proposed which exploits known results on proper vertex colourings in graph theory. Examples are provided to illustrate the results and construction strategies. Particular consideration is given to the special case of designs with blocks of size four and tables of designs are given for this block size.