Networked embedded systems used in many real-time (RT) applications rely on dependable communication. Controller Area Network (CAN) has gained wider acceptance as a standard in a large number of applications, mostly due to its cost effectiveness, predictable performance, and its fault-tolerance capability. Research so far has focused on rather simplistic error models which assume only singleton errors separated by a minimum inter-arrival time. However, these systems are often subject to faults that manifest as error bursts of various lengths which have an adverse effect on the message response times that needs to be accounted for. Furthermore, an important factor to be considered in this context is the random nature of occurrences of faults and errors, which, if addressed in the traditional schedulability analysis by assuming a rigid worst case occurrence scenario, may lead to inaccurate results. In this paper we first present a stochastic fault and error model which has the capability of modeling error bursts in lieu of the commonly used simplistic error assumptions. We then present a methodology which enables the provision of appropriate probabilistic RT guarantees in distributed RT systems for the particular case of message scheduling on CAN under the assumed error assumptions