A method and diagnostic device are disclosed which can receive process variable values (x(t)) of a process variable of a process medium of a process, and extract and record measurement statistics data from such process variable values, which are measured during a measuring phase. Training statistics data can be extracted and recorded from such process variable values, which are measured during a training phase. The measurement statistics data can be compared with training statistics data recorded before the measurement statistics data. The training statistics data can include a training empirical statistical distribution, which can be a distribution of a function of process variable values, which are measured during a training phase, or a distribution of a function of coefficients X.sub.t(k), which are coefficients of a function of a transform of process variable values (x(t)), which are measured during a training phase.