Aspects of statistical quality control of products: choice of criteria for uniformity of dispersions

Analysis and data processing methods allowing to identify nature of the obtained data and their interrelation quickly and accurately are widely demanded now. To identify the relationship between input and output variables, a researcher faces regression analysis tasks, in particular, the estimation of unknown parameters of regression models. In this case application of classical methods is limited by a number of assumptions, in particular, distribution heterogeneity on the measurement region. Using of various stable, nonparametric and adaptive estimation methods in the presence of heterogeneity in the random errors distribution has not been sufficiently studied on the measurement region, therefore the isolation of homogeneous sub-regions in the general heterogeneity measurement region could help to solve the problem of parameter estimation. The criteria for testing homogeneity hypotheses are very often used in various applications of the problems of statistical analysis. In this case we can talk about testing distribution homogeneity hypotheses corresponding to the samples being analyzed or about mean homogeneity or about variances homogeneity. The aim of the study is to investigate the power of parametric and nonparametric criteria under various competing hypotheses.