An algorithm for constructing integral quality indicator of complex systems for a sequence of observations

In the paper we propose an algorithm of constructing the integral characteristics of changes in the quality system based on the recorded measurements. The algorithm provides allotment signal in a multidimensional array of data in terms of a priori uncertainty on the basis of the specified signal-to-noise ratio. Constructing of latent integral characteristics of changes of the quality system on the basis of statistical indicators for a number of consecutive observations is based on the principal component method, taking into account the presence of noise in the measured data (SNR-based algorithm). In classical PCA informativity of integral characteristics is given a priori and is provided by selecting the number of principal components. In the proposed algorithm the information content of the solution is evaluated a posteriori on the basis of variance criterion and the selected parameter signal-to-noise ratio. Based on the proposed algorithm we construct integral indicators of the quality of life of subjects of the Russian Federation for the years of 2007-2014.