Optimal designs of experiments for non-isothermal kinetic rates: analysis of different strategies

We consider the dependence on the measurement schedule of optimal experiments for kinetic parameters when the rates are temperature-dependent and follow the Arrhenius law. We compare three different approaches using the D-optimality criterion: (1) a locally optimal design based on a sequence of four batches where the process is observed at a single time; (2) two batches carried out at constant temperature where the process is observed at a pre-defined grid of times; and (3) a single batch where the temperature profile is optimal regarding the amount of information extracted and the process is observed at a pre-defined grid of times. An extension of the generalized equivalence theorem of optimal experimental design provides insight into the structure of the designs we find. The local D-optimality of the designs obtained is validated using the extended theorem for the latter two approaches.