Improvement of the methodology for determining unproductive loss of time in the disbandment system

. The purpose of the work is to improve the methodology for determining inefficient time losses in the distribution system of the sorting station. Systematic analysis, analytical, graphic modeling, the law of normal distribution and methods for comparing the performance of wagon standing times were used. Unproductive time losses in the disbandment system were determined by the elements of the time spent by wagons at the sorting station. In the sorting station distribution system, the methodology for determining the time of stay and inefficient time losses of transit recyclable cars has been improved using the law of normal distribution. The analysis of unproductive time losses in the receiving and rolling stock of the sorting station by the actual average daily and average monthly values of the elements of unproductive time losses allows not only to purposefully identify methods to reduce the time spent by wagons, but also to carry out an accurate assessment of the work of the station staff, as well as to adjust the norm of the time spent by wagons.


Introduction
Analysis, evaluation and reduction of the time spent by wagons in the operation of any sorting station, especially in the disbandment system, plays an important role for the development of measures to improve technological processes and effectively organize the work of the entire complex for the processing of wagon traffic [1][2][3][4][5][6][7][8][9][10].
It is known that after the arrival of the train from the processing in the arrival park, the wagons fall into the disbandment system, which includes the arrival park and the slide [2,6,7,10]. The main operations in the disbandment system are, processing and disbanding of trains. In addition, the wagons are involved in the following additional operations: securing and fencing of trains, waiting for processing and waiting for disbandment. The sequence of operations in the disbandment system is shown in Figure 1, according to the ДО-24ВЦ reporting form [2,[6][7][8]. In the theory and practice of operational work, the correct establishment of the norm of the time spent by wagons at the station, including in the disbandment system, as well as the development of determination methods are always considered relevant. However, its actual values sometimes deviate from their planned values [2,3,6,7]. The reason for such a deviation in the disbandment system can be many reasons for losses [1,2,4,5]. Therefore, in this work, the analysis of the time spent by transit wagons with processing in the disbandment system is carried out, which in order to more accurately determine the standards of idle time of wagons at the station.
To eliminate these drawbacks, a piecemeal analysis of unproductive time losses is necessary.

Methods
At this moment, the time spent by transit wagons with processing in the disbandment system is reflected in the analytical report on the operation of sorting stations (ДО-24 ВЦ) [2,[6][7][8], that is, from the moment of arrival to the end of disbandment, consists of the following elements t s.disb. = t sec.fence. + t wait proc + t proc + t wait disb + t disb , hour There t sec.fence. − time to secure and fence the train in the reception park (from the moment of arrival at the station to the installation of the train fence), hour; t wait proc − waiting for processing (from the installation of the fence to the beginning of the processing of the composition), hour; t proc − composition processing (from the beginning of composition processing to its end), hour; t wait disb − waiting for disbandment (from the end of the processing of trains to the hitching of the shunting locomotive to move onto the sorting hill), hour; t disb − time to disband trains from the sorting hill, hour.
In the formula, the third and fifth terms are determined by the technology of work in the disbandment system, then the first and second depend on the ratios of the intensity and unevenness of the arrival of trains and the number of performers of the maintenance point, and the fourth depends on the ratio of the processing intervals and the hill interval, as well as their fluctuations.

Results and discussion
The object of the study is the time spent by transit wagons with processing and unproductive time losses, the system of disbanding the sorting station of the Ch, Uzbek railways was taken.
In the course of the work, the actual values of the time spent by transit wagons with processing in the disbandment system were analyzed, for the month of January 2023, therefore, the share of unproductive time losses was determined by comparison with the planned values (Table 1). The graph of the distribution of average daily unproductive time losses in the disbandment system for January to the months of 2023 is shown in Figure 2. It can be seen from Table 1 and Figure 2 that the average daily unproductive time losses in the disbandment system fluctuates on average within 0.2 hours. Therefore, in this paper, the analysis of random variables of the time spent by transit wagons with processing, including their constituent elements, in the disbandment system based on the data of the sorting station H, which is used to determine unproductive time losses. To analyze the time spent by transit wagons with processing in the disbandment system, a statistical distribution series is constructed ( Table 2).
The grouping interval [9] in each digit is determined by dividing the entire range of interval changes by the number of digits  Statistical probability is determined by the formula There n i − the number of observations of a random variable t i .
As a result of the analysis, the distribution law and numerical characteristics of these distributions, such as mathematical expectation, variance, mean square deviation and coefficient of variation, are determined.
The average value (mathematical expectation) of the interval is determined by There ∑ t i ′ ⋅ n i − time occupied by intervals of this category. The variance characterizes the deviation of the actual intervals from their average value and is determined by the formula There t i ′ − t̄− the values of the deviations of the intervals from the average value. The square root of the variance is the mean square deviation of the intervals from the mean value The coefficient of variation is the ratio of the mean square deviation to the mean value The calculation results and numerical characteristics of the time spent by transit wagons with processing in the disbandment system are shown in Table 3.  Table 3 shows that the value of the coefficient of variation varies from 0.07 to 0.22. This allows us to make a suggestion that the distribution of the time spent by transit wagons with processing in the disbandment system can be approximated about its normal distribution.
The validity of the approximation of the time spent by transit wagons with processing in the disbandment system by the normal law according to the above dependence can be checked by the criterion of consent to. Pearson (χ 2 (x-squared) agreement criterion) [9]. The value of χ 2 is determined by the sum of the ratio of the squares of the deviations of the frequencies of theoretical n i * from statistical n i distributions to the frequencies of the theoretical distribution There n i , n i * − accordingly, the statistical and theoretical probabilities of finding a random variable in the i interval.
The procedure for making calculations according to the χ 2 consent criterion is given in Table 4.  The theoretical probability is determined by the formula There f(t) − densities of the normal distribution. The density of the distribution of [9] intervals for the normal law is determined by the formula The theoretical number of observations of a random variable is determined by the formula − the total theoretical number of observations. Figure 3 shows a histogram of the statistical and the curve of the theoretical normal distribution of the time spent by transit wagons with processing in the disbandment system. It can be seen from the figures that the statistical and theoretical distributions are close and the results obtained from statistical data practically coincide with the results calculated according to the laws of distribution.

1)
2) 3) 4) As can be seen from Figure 3, by the appearance of the histogram and by the magnitude of the coefficient of variation, the time spent by transit wagons with processing in the disbandment system can be suggested about its normal distribution. Figure 4 shows the distribution functions of unproductive time losses of elements in the disbandment system.  disbandment expectation М(t) = 0,620 hour, variance D(t) = 0,002 hour and standard deviation σ(t) = 0,042 hour. in the disbandment system, the mathematical expectation is М(t) = 3,395 hour, the variance is D(t) = 0,004 hour and the standard deviation is σ(t) = 0,066 hour.

5)
The analysis shows that in order to further develop a methodology for determining the time of unproductive losses at stations, it is advisable to operate with the average value of the results obtained ( Fig. 3 and 4).
Approximations about the consistency of the statistical and the curve of the theoretical normal distributions were made according to the criterion of V.I. Romanovsky [10]. According to V.I. Ramonosky's rule: if then it is assumed that the adopted distribution law satisfactorily describes the statistical distribution.
there r − number of degrees of freedom, r = k − s; k − number of grouping intervals; s − the number of independent conditions (for a normal distribution, [10] is assumed).
During the verification, using the V.I. Romanovskaya criterion, the following results were obtained for compliance with the normal distribution law of the time spent by transit wagons with processing in the disbandment system, presented in Table 5. Waiting for processing 0.53 < 3 3 Composition processing -0.08 < 3 4 Waiting for disbandment 1.52 < 3 5 Disbandment 1.16 < 3 It can be seen from Table 5 that in all cases, the verification of the belonging of the distribution of random variables of the elements of the time spent by transit wagons gave positive results. This indicates that the approximation of the normal distribution law of the time spent by transit wagons with processing in the disbandment system does not contradict the submitted observation.
Based on Table 4, the proportions of average daily unproductive time losses were determined by comparison with the planned values. The results of the analysis of unproductive time losses in the disbandment system are presented in the form of a histogram in Figure 5. As can be seen from Figure 5, the time loss of transit wagons with processing in the disbandment system includes 5 elements, 3 of which are unfulfilled, which means they should, tends to zero Unproductive time losses in the system of disbanding in anticipation, and the end of technological operations have a significant impact on the performance of the indicator of the time spent by transit wagons with processing.

Conclusions
A piecemeal analysis of the time spent by transit wagons in the disbandment system showed that unproductive time losses are random continuous quantities obeying the normal distribution law.
Thus, for further development of the methodology for determining unproductive time losses in the disbandment system, it is possible to operate with the average values of the results obtained. Therefore, in order to increase the efficiency of the sorting station's operation technology, it is proposed to introduce the parameter of unproductive time losses (t unpr.loss ), into formula (1), which takes into account the duration of losses in the disbandment system t s.disb. = t sec.fence. + t wait proc + t proc + t wait disb + t disb + t unpr.loss , hour There t unpr.loss − duration of the value of unproductive losses, hour.