Distribution of the modified statistic in the two-sample problem

Abstract

At a time when modern production reaches colossal proportions, huge funds are spent on experimental research and testing of construction structures and materials with a view to their further technological improvement. Reducing such costs, accelerating ongoing research and optimizing the process of analyzing test results are significant challenges in the development of modern science. Due to the destructive nature of many tests, it is not possible to measure two or more parameters on the same object. The solution of such important tasks as reducing the duration of tests, calculating reliability in an alternating mode, and reproducing operating modes in laboratory conditions requires knowledge of functional, correlation and a number of other dependencies. These and other reliability problems led to the need to plan accelerated tests, according to the results of which it would be possible to test various hypotheses about simultaneously unobservable parameters. In many problems of the theory of accelerated testing, it is required to check the presence of a functional relationship between failures of construction products in various operating modes. This paper proposes a different approach to solving such a problem, which makes it possible to optimize the process of statistical analysis.