A criterion for optimality of design of evop-type experiments—II. Modified criterion for non-quadratic response surfaces

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Abstract

The response surface is modelled by a function in which some transformed response is a quadratic function of the process variables. The class of transformations used is that of Box and Cox[1], in which the actual transformation is defined by a single parameter λ, unknown a priori. The relevant Bayesian analysis is indicated, after which an expected quadratic approximation to the response surface in the vicinity of the optimum is developed. The procedure of the previous paper[5] can be applied to this approximation, but the posterior variances now include terms representing uncertainties in both parameters and model. The resultant criterion is similar to that for pure quadratic surfaces, but contains extra terms in the ‘D’ matrix, one of which terms is non-linear (but easily linearized).

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