32 Software System for Simulation and Research of Probabilistic Regularities and Statistical Data Analysis in Reliability and Quality Control Ekaterina V. Chimitova, Boris Yu. Lemeshko, Stanislav B. Lemeshko, Sergey N. Postovalov, and Andrey P. Rogozhnikov Novosibirsk State Technical University, Novosibirsk, Russia Abstract: The computer approach to the investigation of estimation methods and statistical tests is considered as an effective technique for developing apparatus of ap- plied mathematical statistics. It has been shown that basing on the considered approach and software system one can investigate statistical properties of estimates for distri- bution parameters including estimates by grouped and censored samples. The statistic distributions of nonparametric goodness-of-fit tests in testing composite hypotheses have been investigated. The statistic distributions and the power of χ 2 goodness-of-fit tests have been investigated depending on the number of intervals and the grouping method. A number of tests for deviation from the normal distribution law have been investigated. Homogeneity tests (for testing hypotheses about equality of means, equal- ity of variances and homogeneity of distributions) have been studied. Various classical tests have been investigated in case of non-normal distributions of observations. Keywords and phrases: Computer simulation, Nonparametric goodness-of-fit tests, χ 2 goodness-of-fit tests, Normality tests, Tests for homogeneity of distributions, Tests for homogeneity of means, Tests for homogeneity of variances, The test power 32.1 Introduction The practice of using statistical analysis methods in applications is full of various prob- lems whose statements are not described within the framework of classical assumptions. A wide range of statistical methods are based on the assumption of measurement error normality. Under real conditions normality and often some other assumptions are not satisfied. The use of classical methods of mathematical statistics in such situations can turn out to be incorrect. Many classical results have an asymptotical nature. At the same time in practice one usually works with samples of a limited size. The application of asymptotical results is not always valid for limited sample sizes. The form of data (measurements) registration doesn’t often conform to complete samples considered in mathematical statistics textbooks. Actually, samples of V.V. Rykov et al. (eds.), Mathematical and Statistical Models and Methods in Reliability: 417 Applications to Medicine, Finance, and Quality Control, Statistics for Industry and Technology, DOI 10.1007/978-0-8176-4971-5 32, c  Springer Science+Business Media, LLC 2010