As vehicular safety functions that intervene in dangerous driving situations use sensor measurements for interpreting the driving situation, they are typically very vulnerable to sensor imperfections and measurement errors have a negative impact on both the safety and the satisfaction of the customer. Therefore, a new methodology for the robust design of an automatic emergency braking (AEB) system is proposed, which considers sensor measurement errors, selects the best decision rule used by the function of the AEB system for triggering an emergency brake intervention and covers several scenarios in which the designed AEB system is supposed to work. The robust function and sensor design for the AEB system is formulated as optimization problems based on a stochastic model. Numerical examples illustrating the elaborated theoretical results show how the new design methodology provides the designer with design spaces from which the optimal parameter values are chosen, with a ranking of the decision rules based on which the best decision rule is selected and with the worst cases from the set of considered scenarios. Moreover, the proposed design methodology generalizes and can be applied to design functions and sensors of other vehicular safety systems as well.