As will be shown the current use of Desirability Indices for optimisation purposes in experimental design gives biased results in general. Researchers were satisfied with approximative solutions as unbiased results would have required analytical expressions for the distributions of Desirability...

A method for constructing approximative tests for arbitrary linear hypotheses on variance components in unbalanced mixed linear models is derived. The idea of cell mean models is used to derive independent and x2 - distributed mean squares. These modified mean squares are combined to generalized...