New Method for Calibrating a Complex Equipment: Creation of the Confidence Tube for Fractal-Like Noise

In this paper, we suggest a new method for the quantitative "reading" of different calibration curves with the help of the so-called procedure of optimal linear smoothing (POLS), and the fractal compression of the measured initial curve thanks to its reduction to three incident points (y max (b), y mean (b), y min (b)), depending on the chosen compression coefficient b from the interval [3,10], and elimination of the smoothed trend. This procedure helps to obtain the trendless sequence (TLS). Then this sequence is split into positive/negative parts and the subsequent summation of the positive and negative amplitudes helps to obtain finally the "confidence tube" (CT) that determines the sensitivity of the measured calibration curve to different external factors. The range of the CT determines its quantitative value. The proposed method increases the sensitivity of the given equipment by two or three orders of magnitude because of the elimination of the calibration curve trend and allows to test stability and reproducibility of the equipment thanks to comparison of the ranges of CT during the measurement process. The proposed method was tested on "Agilent" equipment (in terms of the scattering parameter S 11 ) and the obtained results can lead to reconsideration of some concepts of the conventional metrological standards