For priority based buses such as CAN, worst case response time analysis is able to determine whether messages always meet their deadlines. This can include system models with bounded network faults. However, the worst-case scenario (the critical instant) used by the analysis is extremely pessimistic compared to the rest of the invocations in the hyperperiod. We use weakly hard constraints to provide upper bounds on the maximum number of missed deadlines under fault conditions. By allowing some deadlines to be missed (around the critical instant) the weakly-hard schedulability of the system can be guaranteed at much higher levels of faults. This paper presents a response time based formulation that provides a guarantee on the weaklyhard schedulability of messages. Simulation results based on CAN and the Latest Send Time-CAN protocol show that because of the pessimism of the approach, in fact almost all messages meet their deadlines.