ABSTRACT
In recent years, it has become popular in manufacturing industries to use fractional factorial designs to study a large number of factors for industrial experimentation so as to reduce variability, cost, time, and optimize manufacturing processes. However, when the total number of factors increases significantly, the design will develop confounding problems whereby the effects of one factor or two factor interactions are confounded with each other. In this chapter, we implement a general algorithmic approach (Li, Li, and Ayeni, 1999) for the construction of optimal balanced experimental designs. It is to be noted that many existing optimal designs are not balanced, and the unbalanced nature of these designs can be disadvantageous in practice, leading to an incorrect estimate of effects due to collinearity between factors or due to confounding issues. In order to address these issues, we recommend the use of a column-wise-pairwise (CP) algorithm to generate optimal designs. The two novel ideas in the algorithm are to interchange columns instead of rows and to exchange pairs instead of searching over all candidates, from which comes the name column-wise-pairwise algorithm.
