Optimizing the test power for a radiation retention model in the human body

Design of experiments for zeroth and first-order reaction rates

This work presents optimum designs for reaction rates experiments. In these experiments, time at which observations are to be made and temperatures at which reactions are to be run need to be designed. Observations are performed along time under isothermal conditions. Each experiment needs a fixed temperature and so the reaction can be measured at the designed times. For these observations under isothermal conditions over the same reaction a correlation structure has been considered. D-optimum designs are the aim of our work for zeroth and first-order reaction rates. Temperatures for the isothermal experiments and observation times, to obtain the most accurate estimates of the unknown parameters, are provided in these designs. D-optimum designs for a single observation in each isothermal experiment or for several correlated observations have been obtained. Robustness of the optimum designs for ranges of the correlation parameter and comparisons of the information gathered by different designs are also shown.