The article proposes a nonparametric criterion of the Kiefer — Gihman type to test the Cox model validity for several progressively censored samples. As estimates of the reliability function for each sample we are using the Kaplan — Meyer ones. The paper proves that if the hypothesis is valid, the Kiefer — Gihman distribution can be used as an approximation of the asymptotic distribution of the criterionstatistics. Based on the particle random walk model over a multidimensional cells array, the paper has developed the method for calculating the exact statistics distributions. The article presents obtained probability values tables of the proposed statistics exact distributions for a wide range of samples possible values. Statistical modeling methods show Cox parameters estimating method consistency, based on the statistics minimization. We present the obtained estimates histograms for the developments exponential distribution to failure. The research results are used when analyzing the redundant technical systems of different multiplicity tests results operating in different operating conditions.
Analyzed systems find applications in all industries — from machine building to radio electronic.
Timonin V., Tyannikova N. Cox model validity checking for several progressively censored samples. Маthematical Modeling and Coтputational Methods, 2017, №1 (13), pp. 102-117
The article considers the problem of testing the Lehmann power hypothesis for two censored samples. The Kolmogorov — Smirnov type criterion based on a comparison of the Kaplan — Meier type estimates of the distribution functions for each censored sample is developed to test the power hypothesis. A method for calculating the exact statistics distributions is described on the basis of the model of particle random walk over an integer lattice. The probability values are calculated for a wide range of possible sample sizes. The convergence of this statistics distribution to the standard Kolmogorov — Smirnov distribution is proved provided that the hypothesis being tested is valid. The properties of a power parameter estimate obtained by minimizing statistics are investigated by statistical modeling methods.
Тимонин В.И., Тянникова Н.Д. Методы решения задачи непараметрической проверки гипотез Лемана при испытаниях параллельных систем. Математическое моделирование и численные методы, 2018, № 1, с. 98-112
This paper considers the problem of function estimating for times to failure translation from one mode to another. This problem arises, for example, when there is data on failures of products in vitro tests and you need to estimate the reliability of the same type products with actual test conditions. For simplicity, we consider the case where MTBF have linear relation. The proposed method is based on minimizing the Kolmogorov-Smirnov statistic, which is used to test the homogeneity of two progressively censored samples. A special feature of the proposed statisticis using the Kaplan-Meier estimates of the reliability function for each sample. Provided conjecture homogeneity of two samples, the distribution of statistics does not depend on the type of distribution of failures. This paper proposes a method for calculating the exact distributions of these statistics. Tables of exact distributions probabilities are presented for a wide range of possible values of the volumes of samples. By means of statistical modeling a table of acceleration factor values is calculated and its histograms are presented.
Keywords: non-parametric statistics, the Kolmogorov-Smirnov test, Kaplan-Meier estimate, progressive censoring.
Timonin V., Tyannikova N. Progressively censored sample comparison - numerical methods for homogeneity statistic distributions and study of communication parameters estimating by Monte Carlo method. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 89-100