A process for monitoring a machine, within the framework of a FMEA process for at least one component of the machine for at least one predetermined fault which can be diagnosed by means of a diagnosis diagram and a diagnosis system with sensors for detecting physical parameters of the machine, a diagnosis priority number being determined which is the product of the following index quantities: severity of the effect of occurrence of the fault with respect to the serviceability of the machine; expected machine-specific consequential costs when a fault occurs, and the possibility of correction of the fault. The diagnosis priority number is used in the evaluation of the diagnosis diagram, the diagnosis system, the current machine state, the necessary maintenance measures and/or the failure risk of the machine.