Deconvolution-based methods to extract uncertainty components

Abstract

Abstract A measurement result is supposed to provide information about the distribution of values that could reasonably be attributed to the measurand. However, in general, it provides the distribution of values returned by the employed measuring system, when the measurand is given as the input quantity to this system. This distribution of values is mathematically given by the convolution of two probability density functions (PDFs): the one representing the actual distribution of values of the measurand and the one representing the uncertainty contribution of the employed measuring system. In principle, if the uncertainty contribution of the measuring system is known, the distribution of values that could reasonably be attributed to the measurand can be obtained by applying a proper deconvolution algorithm: this distribution is, indeed, the one of interest in any industrial measurement process. Similarly, if the PDF representing the distribution of values of the measurand is known, the PDF representing the uncertainty contribution of the measuring system to the resulting distribution of values returned by the instrument can be obtained by applying a proper deconvolution algorithm: this distribution is, indeed, the one of interest when a calibration is performed. In practical situations, deconvolution algorithms provide rather inaccurate results when applied to PDFs, especially when they are experimentally obtained from histograms of collected data. This paper proposes a deconvolution method, based on the use of Fuzzy variables (or Possibility Distributions) to represent distribution of values, which proves to provide much more accurate results. Simulation results, as well as experimental results are discussed to validate the proposed method.