A Bayesian design criterion for locating the optimum point on a response surface

Most factorial experiments in industrial research form one stage in a sequence of experiments and so considerable prior knowledge is often available from earlier stages. A Bayesian A-optimality criterion is proposed for choosing designs, when each stage in experimentation consists of a small number of runs and the objective is to optimise a response. Simple formulae for the weights are developed, some examples of the use of the design criterion are given and general recommendations are made.