Expected Design Space: a Bayesian perspective based on modelling, prediction and multi-criteria decision method

The Design Space (DS) is defined as the set of factors settings (input conditions) that provides results at least better than pre-defined acceptance limits. The proposed methodology aims at identifying a region in the space of factors that will likely provide satisfactory results during the future use of an analytical method or process in routine, through an optimization process.

First, in a Bayesian framework, DS is derived from the joint predictive posterior distribution of the responses in a multivariate multiple regression problem using non-informative as well as informative prior distribution of the parameters. The case of DS in presence of highly correlated responses will be covered.

Second, a multi-criteria decision is taken with respect to the pre-defined acceptance limits, aiming to identify the DS of any analytical methods or other processes. A strong link is made between acceptance limits and objective functions to optimize, using desirability functions and index.

Examples based on high-performance liquid chromatography (HPLC) methods will be given, illustrating the applicability of the methodology with highly correlated and constrained responses.