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Calculation Method of the Distribution Statistics of Kolmogorov-Smirnov Type in Testings with Alternate Load for Finite Sample Size

Authors: Timonin V.I., Tyannikova N.D. Published: 04.10.2014
Published in issue: #5(56)/2014  
DOI:

 
Category: Mathematics and Mechanics  
Keywords: accelerated testing, testing in alternative modes, non-parametric statistics, Kolmogorov-Smirnov statistics, Kaplan-Meier estimates

In theory, the accelerated tests are implementing using widely the testings in an alternating mode. These testings are designed to determine the same scaling functions for recalculating of the accelerated tests results to the normal mode for any parts of single-type products. An improved method for testing in an alternating mode is proposed that allows estimating scaling functions for the recalculating with higher accuracy. The calculation method of the exact distributions statistics of Kolmogorov-Smirnov type designed to test hypotheses about the form of link function is given. The feature of these methods is the application of the Kaplan-Meier estimation of the reliability function to reduce the amount and duration of the alternative modes testings. Knowledge of the exact distributions of applied statistics is important due to the fact that in reality there are no large sample size of products allocated for testings. However, in most cases the asymptotic distributions of the statistics are used. It often leads to large errors in the analysis of test results. The proposed method can eliminate this drawback.

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