Fault diagnosis is routinely carried out with the aid of the various data processing methods, yet the relations between the normal state and different faulty states are considered less, which should be the major concern of the diagnosability issue. In this paper the probabilistic derivation of diagnosability is presented for the faults containing uncertainties, and a method for analyzing system-level quasi real-time diagnosability is given. The stochastic characterizations of different fault modes are extracted and a measurement based on the modified distance is established to quantify diagnosability performance. Diagnosability includes detectability and distinguishability, and the two parts are the same in essence that they both identify the distinction of two different states. The operational diagnosability is also addressed in the quasi real-time setting where the system-level diagnosis is carried out with the state data of the critical components. Finally, the method is applied to a single-stage vapor compressor refrigeration cycle system to exemplify how to analyze diagnosability of a system dynamic with the input data from its critical component. (C) 2014 Elsevier Ltd. All rights reserved.