Optimal diallel cross designs for the interval estimation of heredity

Available results on optimal block designs for diallel crosses are based on standard linear model assumptions where the general combining ability effects are taken as fixed. In many practical situations, this assumption may not be tenable since often one studies only a sample of inbred lines from a possibly large (hypothetical) population. In this paper, a random effects model is proposed that allows us to obtain an interval estimate of the ratio of variance components. We address the issue of optimal designs by considering the L-optimality criteria. Designs that are L-optimal for the estimation of heredity are obtained in the sense that the designs minimize the maximum expected normalized length of confidence intervals. The approach leads to certain connections with an optimization problem under the fixed effects model.