I-optimal design of split-plot mixture-process variable experiments: A case study on potato crisps

Designed experiments are powerful tools when developing new products or processes. They allow changing the settings in a systematic way such that a minimal experimental effort results in maximal information. In the food industry, performing designed experiments can be challenging because products and processes are often complex and involve many factors of different kinds. Moreover, some of the factors (for instance, the ingredients of a new formulation) may have intrinsic properties that can be measured but cannot be changed. These are referred to as pre-specified factors or covariates. In this paper, we discuss a representative case study and show how these complications often encountered in the food industry are handled. The goal of the case study is to lower the lipid content of potato crisps by means of a split-plot type of designed experiment involving a complex mixture of ingredients, various constraints on the proportions of the mixture ingredients, and a limited number of batches that each come with a set of covariates. We show how our approach provides insight into the most important factors and allows the product quality to be optimized in an efficient way.