### Data reliability of the CAN protocol Residual error probability as a function of bit error probability

The introduction of safety-related systems in automobiles brought with it high requirements for the reliability of data transmission. The objective is frequently formulated as not permitting any dangerous situations for the driver to occur as a result of data exchange throughout the whole life of a vehicle.

This goal is achieved if the reliability of the data is sufficiently high or the residual error probability is sufficiently low. In the context of bus systems data, reliability is understood as the capability to identify data corrupted by transmission faults. The residual error probability is a statistical measure of the impairment of data reliability: it specifies the probability that data will be corrupted and that this corruption will remain undetected. The residual error probability should be so small that on average no corrupted data will go undetected throughout the whole life of a system.

Calculation of the residual error probability requires that the errors which occur be classified and that the whole transmission path be described by a model. If we determine the residual error probability of CAN as a function of the bit error probability for message lengths of 80 to 90 bits, for system configurations of, for instance, five or ten nodes and with an error rate of 1/1000 (an error in one message in every thousand), then maximum bit error probability is approximately 0.02 - in the order of 10-13. Based on this it is possible to calculate the maximum number of undetectable errors for a given CAN network.

For example, if a CAN network operates at a data rate of 1 Mbit/s, at an average bus capacity utilization of 50 percent, for a total operating life of 4000 hours and with an average message length of 80 bits, then the total number of messages transmitted is 9 x 1010. The statistical number of undetected transmission errors during the operating life is thus in the order of less than 10-2. Or to put it another way, with an operating time of eight hours per day on 365 days per year and an error rate of 0.7 s, one undetected error occurs every thousand years (statistical average).