The construction of simultaneous optimal experimental designs for several polynomials in the calibration of analytical methods

In this paper a criterion is described for the construction of experimental designs for the evaluation of calibration models in analytical chemistry. The proposed criterion seeks a compromise between the D-optimal designs for estimating the parameters of different polynomial models. A computer algorithm is presented for a sequential construction of experimental designs using the optimality criterion. The performance of the optimality criterion and the computer algorithm is elaborated for the problem of discrimination between a first- to a third-degree polynomial for the calibration of analytical methods. An experimental design consisting of replicate measurements at five distinct levels equally spaced over the calibration range proved a good solution.