Mathematical methods for reliability verification of data on reliability of locomotives, their operation and maintenance

In the practice of railway transport and the locomotive complex, the average statistical data used in practice are not homogeneous, which is usually called “average temperature in the hospital” in the literature. The homogeneity of data is determined by their unimodality, i.e. the presence of one process in the sample. Unsuccessful sampling leads to its bimodality and even multimodality. It is proposed to check for unimodality of the initial data using 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 distribution laws of a random variable: normal, exponential, lognormal, or another known law. Therefore, any unimodal sample must meet the goodness-of-fit test, which the article proposes to use the Pearson test (“chi-square”, χ2). The unimodality of the data is proposed to be estimated through the probability of compliance with the law of distribution of a random variable chosen for consideration, considering the probability of more than 0.3 (30%) to be sufficient. On the example of locomotive operation data and on-board microprocessor systems data, data are shown that cannot really be unimodal, but there is data that requires 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 traffic (main traffic, shunting or switching work), unimodality is achieved. An attempt to enlarge the data (take several series, several polygons, etc.) leads to the loss of unimodality. The article considers the unimodality of these on-board microprocessor control systems MSU-TP for diesel locomotives of the 2TE116U series. The expected operating time for the positions of the driver's controller turned out to be multimodal data. Unexpectedly, the current of the traction motors turned out to be unimodal, regardless of the driving position of the driver's controller.