A method and system for monitoring an industrial process and a sensor. The method and system include generating a first and second signal characteristic of an industrial process variable. One of the signals can be an artificial signal generated by an auto regressive moving average technique. After obtaining two signals associated with one physical variable, a difference function is obtained by determining the arithmetic difference between the two pairs of signals over time. A frequency domain transformation is made of the difference function to obtain Fourier modes describing a composite function. A residual function is obtained by subtracting the composite function from the difference function and the residual function (free of nonwhite noise) is analyzed by a statistical probability ratio test.