Industrial communication networks like the Controller Area Network (CAN) are often required to operate reliably in harsh environments which expose the communication network to random errors. Probabilistic schedulability analysis can employ rich stochastic error models to capture random error behaviors, but this is most often at the expense of increased analysis complexity. In this paper, an efficient method (of time complexity O ( n l o g n ) ) to bound the message deadline failure probabilities for an industrial CAN network consisting of n periodic/sporadic message transmissions is proposed. The paper develops bounds for Deadline Minus Jitter Monotonic (DMJM) and Earliest Deadline First (EDF) message scheduling techniques. Both random errors and random bursts of errors can be included in the model. Stochastic simulations and a case study considering DMJM and EDF scheduling of an automotive benchmark message set provide validation of the technique and highlight its application.