A new methodology to robustify an experimental design: Application to the Baranyi model

Abstract

A robust experimental design is a desired object for practitioners when there is uncertainty about any of the assumptions necessary to compute the optimal design. For instance, when they use non-linear models, which requires having nominal values of the parameters. Several alternatives have been developed in the literature to obtain robust experimental designs such as adaptive or Bayesian designs, among others. Here a new methodology is proposed to robustify the optimal experimental design. Based on the maximin idea, the method adds support points to the optimal design, to obtain designs that are robust. It is applied to the Baranyi model, one of the most used mathematical models in predictive microbiology to describe the behaviour of microorganisms in food products, an essential issue for human health. Previously, D-optimal designs are provided for the model, considering 4 and 6 parameters to be estimated. A sensitivity analysis is carried out regarding the deviations in the nominal values of the parameters, which shows a greater loss of efficiency for two of them. Given these results, the new methodology is applied to the D-optimal design, checking the robustness of the augmented designs through the efficiency achieved. Finally, c-, A- and I-optimal designs are calculated to provide accurate estimation of the model parameters and the predictions.