Estimation of the average time to failure of the turning steps according to the operation data

The purpose of this study is to determine the empirical law of the distribution of developments to the failure of the turning steps installed on passenger cars of locomotive traction. The correct choice of the distribution law for each technical product allows for the current calculation of reliability indicators, predicting them, as well as developing preventive measures for a specific technical product and leveling costs both during production and during operation.
The article presents well-founded arguments that the failure time for turning steps is characterized by the Weibull distribution law. For confirmation, a statistical criterion for checking the deviation of the distribution from the normal one was applied.
On the basis of carried statistic analysis a histogram of frequencies and a line of the density function of samples of failure time in the data fixation period from 2010 to 2017 were built. Results of applying the 2 agreement criterion in the same software environment revealed that the failure time of the closed turning step comply with the law of Weibull distribution. Authors suggest using the maximum likelihood method to identify Weibull distribution parameters, on the basis of which the value of the point estimate of the mean time to failure is calculated.
Based on the research, it is concluded that this type of distribution law and the process of finding its parameters should be introduced into the program and methodology for assessing the operational reliability of the turning steps, when calculating the average time to failure of the steps, and consider the possibility of applying this law for analogous products.
In conclusion, calculation of the pointed estimation of the average time to failure of the closed turning step was made on the basis of operational tests for one year in accordance with the adopted distribution law.

1. Gnedenko B. V. Nadezhnost' i effektivnost' v tekhnike. Spravochnik: v 10 t. T. 2. Matematicheskie metody v teorii nadezhnosti i effektivnosti [Reliability and efficiency in technology. Reference book in 10 vol. Vol. 2. Mathematical methods in the theory of reliability and efficiency]. Moscow, Mashinostroenie Publ., 1987, 280 p.

2. Kozlov B. A., Ushakov I. A. Spravochnik po raschetu nadezhnosti apparatury radioelektroniki i avtomatiki [Reference book for calculating reliability of radio electronics equipment and automation]. Moscow, Sov. Radio Publ., 1975, 472 p.

3. Polovko A. M., Gurov S. V. Osnovy teorii nadezhnosti. Praktikum [Fundamentals of the theory of reliability. Practical work]. St. Peterburg, BHV-Peterburg Publ., 2006, 560 p.

4. Gnedenko B. V., Belyaev Yu. K., Solov'ev A. D. Matematicheskie metody v teorii nadezhnosti [Mathematical methods in the theory of reliability]. Moscow, Nauka Publ., 1965, 524 p.

5. L’vovskiy E. N. Statisticheskie metody postroeniya empiricheskikh formul. Ucheb. posobie dlya vuzov [Statistical me thods for constructing empirical formulas. Textbook for universities]. Moscow, Higher school Publ., 1988, 238 p.

6. Lemeshko B. Yu. Kriterii proverki otkloneniya raspredeleniya ot normal'nogo zakona [Criteria for checking the deviation of the distribution from the normal law]. Novosibirsk, NITs INFRA-M, 2015, 160 p.

7. Bure V. M., Evseev E.A. Osnovy ekonometriki. Ucheb. posobie [Basics of Econometrics. Tutorial]. St. Peterburg, St. Petersburg University Publ., 2004, 72 p.

8. Bure V. M., Parilina E. M., Sedakov A. A., Shevkoplyas E. V. Prikladnaya statistika v R, Statistica i Excel: opisatel'naya statistika, otsenivanie parametrov, statisticheskie kriterii. Ucheb. posobie [Applied statistics in R, Statistica and Excel: descriptive statistics, parameter estimation, statistical criteria. Tutorial]. St. Peterburg, St. Petersburg University Publ., 2011, 104 p.

9. RD 50-690-89. Methodical instructions. Reliability in technology. Methods for assessing reliability indicators based on experimental data. Put into force 01.01.1991. Moscow, Standard Publishing house, 1990, 136 p. (in Russ.).

10. Kostochkin V. V. Nadezhnost' aviatsionnykh dvigateley i silovykh ustanovok [Reliability of aircraft engines and power plants]. Moscow, Mashinostroenie Publ., 1976, 248 p.