Article 1218

Title of the article

INVESTIGATION OF INTEGRAL ESTIMATES 

Authors

Mikhailov Viktor Sergeevich, lead engineer, Central Research Institute of Chemistry and Mechanics named after D. I. Mendeleev (115487, 16а Nagatinskaya street, Moscow, Russia) Mvs1956@list.ru

Index UDK

621.382.029.6

DOI

10.21685/2307-4205-2018-2-1

Abstract

The purpose of this paper is to construct a rule for choosing an effective estimate based on an integral approach different from the first type. And, on the basis of the constructed criterion, to obtain effective estimates based on the results of the tests conducted in accordance with the plan of type NВτ. Methods. To find an effective estimate, we used the integral numerical characteristics of the accuracy of the estimate, namely, the total square of the displacement (deviation) of the expected realization of a certain valuation variant from all possible values of the estimated characteristic from the different values of the parameter of the Poisson crt characterizing the failure flow of the set of products under test. Results and conclusions. 1. According to the results of tests of type NВτ, integral estimates of type 1 are used in problems when it is required to find an effective estimate with minimum displacement, and integral estimates of the second type – when it is required to find an effective estimate with minimal variance. 2. An ideal option, in estimation problems, is to use an unbiased estimate with minimal variance, if such an estimate exists. Otherwise, we should look for estimates with a minimum bias, and among them – with a minimum variance. Such a search process guarantees the obtaining of estimates with good accuracy characteristics. Therefore, in reliability problems, one should not rely on estimates constructed by minimizing a functional of the second type. 3. The evaluation of mean time between failures 01 T is effective among the 1-type integral estimates proposed by the criterion, and the evaluation of mean time between failures 05 T is effective among the 2- type integral estimates proposed by the criterion. 4. As an estimate of probability of failure-free operation, a traditional unbiased estimate should always be used, except for fail-safe tests. In this case, an effective integral estimation of the one type  θ (R,v,g) = e(g/T06) or an effective integral estimate of the second type of the reliability function θ (R,v,g) = e(g/T01) in depending on reliability problems.

Key words

Poisson distribution law; exponential distribution; test plan; point estimation

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Дата создания: 18.06.2018 14:05
Дата обновления: 18.06.2018 15:07