How to quantify the maturity of production processes

Quantifying the properties of interest is a basic need in all fields of science and engineering. We propose formal definitions to quantify the maturity of production processes. The definitions are inspired by the concepts of controllability and observability from control theory. But instead of a binary classification of a system as controllable/uncontrollable and observable/unobservable, we consider a probability distribution for the remaining error. From the proposed maturity quantification, the remaining potential for optimizations can be evaluated. This is shown for the example of an electric arc furnace (EAF), for which high-fidelity simulation models are available.