The Design of Experiments for Parameter Estimation

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Abstract
This paper is concerned with the design of experiments to estimate the parameters in a model of known form, which may be nonlinear in the parameters. This problem was discussed in detail by Box and Lucas for the case where N, the number of experiments, is equal to p, the number of parameters. The present work is an extension to cases where N is greater than p. Conditions are established under which, when the number of experiments is a multiple of the number of parameters, replication of the best design for p experiments is an optimal design for N experiments. Several chemical examples are discussed; in each instance, the best design consists of simply repeating points of the original design for p experiments. An example is also mentioned where the best design does not consist of such replication.

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