A note on the construction of incomplete row–column designs: An algorithmic approach

Row–column designs are widely recommended for experimental situations when there are two well-identified factors that are cross-classified representing known sources of variability. Row–column designs are expected to result a gain in accuracy of estimating treatment comparisons in an experiment as they eliminate the effects of the row and column factors. However, these designs are not readily available when the number of treatments is more than the levels of row and column blocking factors. Here, an algorithmic approach for constructing a new series of row–column​ designs with incomplete rows and columns, by amalgamating two incomplete block designs has been proposed. A wide range of incomplete block designs, viz., balanced incomplete block designs/ partially balanced incomplete block designs/t-designs, are available in the literature, which can be selected as input designs to construct the proposed series of designs. To avoid the complexity involved in the construction algorithm, an R package “iRoCoDe” has been developed for the generation of the proposed designs. A catalogue of designs has been prepared using “iRoCoDe” for ≤ 20 treatments. Further, a general form of the information matrix of these incomplete row–column​ designs has been derived, and characterization properties of component designs of the final array have been studied. The designs obtained are cost-effective and efficient as they require less experimental resources and have high canonical efficiency factors.