Phase stability calculations consume a significant part of a process or a compositional reservoir simulation CPU time as millions of two- or multi-phase equilibrium calculations on complex multicomponent mixtures need to be performed. The iterative nature of the solving methods involved in conjunction to the risk of false convergence render these computations as a hot research area. A new method is presented for generating discriminating functions of pressure, temperature and compositions which separate stable from unstable mixtures. These functions provide the same stability state predictions as the established minimum tangent plane distance since they exhibit exactly the same sign and zeroing points. Their simple explicit expressions allow for the rapid, non-iterative and robust evaluation of the stability state of the fluid under study. Being generated by using the fluid's Equation of State model they offer predictions which can be as accurate as the thermodynamic model itself. A set of examples demonstrates the accuracy of the proposed method as well as its very significant advantages with respect to computational speed. (c) 2011 Elsevier B.V. All rights reserved.