Publisher Summary Correct identification and elimination of gross errors in plant measurements is a key factor for the performance of industrial on-line optimization. For nonlinear plant models, the gross error detection problem is very challenging. This chapter presents two data reconciliation and gross error detection strategies for nonlinear models: one based on a serial elimination algorithm using a linearized model and another one based on the Tjoa–Biegler contaminated normal distribution approach. The comparison is based upon the results obtained with commercial on-line data reconciliation and optimization package using a rigorous model of two industrial refinery processes. The gross error detection and elimination (GEDE) algorithm presented is illustrated on a gas separation process. The plant consists of a debutanizer, a naphtha splitter, and a de-isohexanizer. The nonlinear model contains 10,858 equations and 11,663 variables (793 variables were fixed). The number of measurements is small in comparison with the problem size, but this is typical for a refinery process, particularly with a rigorous model.