D- and T-optimum designs for the kinetics of a reversible chemical reaction

The purpose of our paper is to exemplify D-optimum designs for parameter estimation in the kinetics of a reversible chemical reaction and to find T-optimum designs for model discrimination, as a method of determining the order of reaction. Although the statistical methods are similar for consecutive and reversible reactions, the designs have markedly different properties. As a chemical example we use the esterification of ethanol and acetic acid. On the basis of this example we discuss the geometrical interpretation of D-optimum designs, which is strictly connected with the course of reaction and permits instructive comparisons of reversible and consecutive chemical processes. The methods of optimum experimental design provide an alternative to conventional designs for parameter estimation and model discrimination. We show how much more efficient the optimum design can be for parameter estimation than relying on a conventional design. We calculate a sequential T-optimum design and propose a statistical test verifying a hypothesis on the order of reaction. We also present the theoretical background of information matrices for non-linear models, D-optimum designs for parameter estimation and T-optimum designs for model discrimination.