A‐optimal model‐based design of experiments for processes with uncertain inputs

Model‐based design of experiments (MBDoE) techniques are tools for selecting experimental conditions that enable accurate parameter estimation for mechanistic models. Most MBDoE approaches assume that the selected experimental conditions will be implemented perfectly, without uncertainties in the independent variables. Unfortunately, some chemical processes have independent variables with uncertainties, which are as important as uncertainties in the process responses. In this study, a new sequential A‐optimal MBDoE method is proposed, which accounts for input uncertainties when selecting new experimental conditions. This methodology relies on an augmented Fisher information matrix that accounts for imperfectly‐known inputs, which are estimated along with the model parameters. The proposed technique is used to design experiments for a batch pharmaceutical process with an uncertain initial reactant concentration. The effectiveness of the proposed method is confirmed using Monte‐Carlo simulations, revealing that more‐accurate parameter estimates are obtained than when a traditional A‐optimal MBDoE technique is used that ignores input uncertainty. The proposed method is easier to use than previous MBDoE techniques that account for input uncertainties. It readily accommodates complex practical situations encountered during development of mechanistic models including situations where some inputs have important uncertainties while others are perfectly known. The new methodology can be used for multi‐response dynamic systems described by differential equations.