This paper presents a quantitative analysis of the model order selection problem, and its application for system identification of an ethylene furnace with open-loop and closed-loop industrial plant data. Empirical ARX models are used to describe the physical phenomena in the ethylene furnace. Appropriate model order selection is done based on the information content in the industrial data from the ethylene plant. Model order is chosen by using Akaike's information criterion (AIC), Rissanen's minimum description length (MDL), and a criterion based on the unmodeled output variation (UOV). UOV results in a smaller order model that has well-defined parameters with tight confidence intervals as compared to AIC and MDL. Similar models are obtained using closed-loop and open-loop data from the industrial process when UOV is used because the models are well-determined. (C) 2003 Elsevier Science Ltd. All rights reserved.