Optimal experimental design for estimating the kinetic parameters of the Bigelow model

The optimum experimental design for systems following the Bigelow model was studied by determining the sampling conditions that lead to a minimum confidence region for a number of observations equal to the number of parameters. For isothermal conditions, it was found that this corresponds to the sampling times when the fractional concentration of the decaying factor (η_i) is equal to e^-1 and that the experiments should be performed in the limit range of temperatures chosen. These results are identical to those described in the literature for a first-order Arrhenius model. For non-isothermal experiments with linearly increasing temperature, the optimal experimental design is obtained with a maximum heating rate, a minimum initial temperature and sampling times when the product of the fractional concentrations is e^-2 (with η₁ ≅ 0.70 and η₂ ≅0.19). The influence of the heating rate on the precision of the estimates is more significant for high z values and the influence of the initial temperature is more significant for low values of the heating rate.