The mean objective cost of uncertainty (MOCU) quantifies the performance cost of using an operator that is optimal across an uncertainty class of systems as opposed to using an operator that is optimal for a particular system. MOCU-based experimental design selects an experiment to maximally reduce MOCU, thereby gaining the greatest reduction of uncertainty impacting the operational objective. The original formulation applied to finding optimal system operators, where optimality is with respect to a cost function, such as mean-square error; and the prior distribution governing the uncertainty class relates directly to the underlying physical system. Here we provide a generalized MOCU and the corresponding experimental design. We then demonstrate how this new formulation includes as special cases MOCU-based experimental design methods developed for materials science and genomic networks when there is experimental error. Most importantly, we show that the classical Knowledge Gradient and Efficient Global Optimization experimental design procedures are actually implementations of MOCU-based experimental design under their modeling assumptions.