A theory is developed for quantifying fault detectability and fault isolability properties of static linear stochastic models. Based on the model, a stochastic characterization of system behavior in different fault modes is defined and a general measure, based on the Kullback-Leibler information, is proposed to quantify the difference between the modes. This measure, called distinguishability, of the model is shown to give sharp upper limits of the fault to noise ratios of residual generators. Finally, a case-study of a diesel engine model shows how the general framework can be applied to a dynamic and nonlinear model.