Row-column response surface designs

Factorial experiments are widely used in industry to investigate the effects of process factors on quality response variables. Many food processes, for example, are not only subject to variation between days, but also between different times of the day. Removing this variation using blocking factors leads to row-column designs. In this paper, an algorithm is described for constructing factorial row-column designs when the factors are quantitative, and the data are to be analysed by fitting a polynomial model. The row-column designs are constructed using an iterative interchange search, where interchanges that result in an improvement in the weighted mean of the efficiency factors corresponding to the parameters of interest are accepted. Some examples illustrating the performance of the algorithm are given.