519.248 Progressively censored sample comparison - numerical methods for homogeneity statistic distributions and study of communication parameters estimating by Monte Carlo method

Timonin V. I. (Bauman Moscow State Technical University), Tyannikova N. D. (Bauman Moscow State Technical University)

NON-PARAMETRIC STATISTICS, THE KOLMOGOROV-SMIRNOV TEST, KAPLAN-MEIER ESTIMATE, PROGRESSIVE CENSORING


doi: 10.18698/2309-3684-2015-3-89100


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.


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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



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