Design Space and desirability index. A Bayesian predictive risk-based approach to flexibly achieve multi-criteria decision methods.

The Design Space (DS) is defined as the set of factors settings (input conditions) that will provide 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. In a Bayesian framework, the responses are modelled using a multivariate multiple regression model allowing deriving their joint predictive posterior distribution. On the basis of this consequent distribution, a multi-criteria risk-based decision is taken with respect to the pre-defined acceptance limits. This aims to identify the DS. In this context, desirability methodologies are also applied to take the risk-based decision in a more flexible way. An example based on high-performance liquid chromatography illustrates the applicability of the methodology with highly correlated and constrained responses