The supervision of process values with regard to critical limits is a common task in process-computer-applications. If measurement-errors are present, then wrong decisions can not always be avoided. It may happen, that limit crossings are not detected immediately, or alternatively, that crossings are reported, though none are present. In this paper a method for process supervision is proposed ... [Show full abstract] which, in a certain sense, is optimal with regard to the risk of wrong decisions. The method is based on mathematical statistics. it is shown, that the supervision in many cases can be accomplished by examination of a linear combination of a sequence of measured values. In spite of the statistical refinements, the on-line computations are still not extensive, compared to other, more usual supervision procedures.