Optimal experimental design for estimating the kinetic parameters of processes described by the weibull probability distribution function

The optimum experimental design for determining the kinetic parameters of the model resulting from the Weibull probability density function was studied, by defining the sampling conditions that lead to a minimum confidence region of the estimates, for a number of observations equal to the number of parameters. It was found that for one single isothermal experiment the optimum sampling times corresponded always to fractional concentrations that are irrational numbers (approximately 0·70 and 0·19) whose product is exactly 1/e². The experimental determination of the equilibrium conversion (for growth kinetics) is very important, but in some situations this is not possible, e.g. due to product degradation over the length of time required. Sampling times leading to a maximum precision were determined as a function of the maximum conversion (or yield) attainable. For studies of kinetic parameters over a range of temperatures, performed with a minimum of three isothermal experiments, it was proved that the optimum design consists of two experiments at one limit temperature with two sampling times (those corresponding to fractional concentrations of approximately 0·70 and 0·19) and another at the other limit temperature for a sampling time such that the fractional concentration is He. Case studies are included for clarification of the concepts and procedures.