Mathematical Methods for Validation of Data on Reliability, Operation and Maintenance of Locomotives

The objective of the article is to describe the method proposed by the authors and intended for validity check of initial data for managing reliability of locomotives and the entire locomotive facilities. It is shown that probabilistic-statistical methods which constitute the basis of Edward Deming’s theory of enterprise variability allowing to control the quality of enterprises’ products, including their reliability.

The averaged statistical data used in practices of railway transport and its locomotive economy are not homogeneous, representing what is called in popular publications «average temperature of hospital patients». The homogeneity of data is determined by their unimodality, i.e., the presence of a single process in the sample. Unsuccessful sampling leads to its bimodality and even multimodality.

The research method proposed in the article is check for unimodality of the initial data based on the consequence of the law of large numbers, according to which, with an increase in the number of data, homogeneous samples tend to one of the laws of distribution of random variable: to normal, exponential, lognormal or other known law. Therefore, and since any unimodal sample must meet a goodness-of-fit test, the article proposes to apply Pearson’s chisquare test (χ2). The unimodality of the data is suggested to be estimated through the probability of compliance with the chosen law of distribution of a random variable considering the probability of more than 0,3 (30 %) to be sufficient.

Using the example of locomotive operation data and on-board microprocessor systems data, data are shown that cannot really be unimodal, as well as the data that require changing the sampling rules to achieve unimodality. For example, when considering the average daily runs of locomotives by series at specific home depots with participation in one type of traffi (main traffi export, or shunting operations), their unimodality is achieved. An attempt to enlarge the data (to consider several series, several polygons, etc.) results in loss of unimodality.

The article considers the unimodality of data of MSU-TP on-board microprocessor control systems for diesel locomotives of 2TE116U series. The expected operating time for the positions of the driver’s controller turned out to be multimodal data. Surprisingly, the current of the traction motors turned out to be unimodal, regardless of the driving position of the driver’s controller.

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