Development of methodology for studying the technological and operational characteristics of forming tools of hot rolling mills (Science journal «Technical service of agriculture, forestry and transport systems», 2026)
It is shown that when conducting research aimed at determining the influence of technological and operational characteristics of forming tools on their resource, a fairly large number of indicators are used. Given that the initial data contain information for different periods of research, there is a need to check the possibility of combining different samples into one for the possibility of forming statistical hypotheses. It is noted that to determine the possibility of combining samples of operational characteristics of rolling rolls for different periods of time, it is advisable to consider two options for approaches: 1 − if data analysis requires the use of random variable distribution functions, for example, for probabilistic assessment of the resource of rolls, then in this case the homogeneity of the two samples is necessary, i.e. equality of distribution functions; 2 − if for data analysis it is sufficient to use only statistics of a random variable (mean value of the analyzed variable, standard deviation, coefficient of variation), for example, when considering the number of installations during the period of operation of the roller, then in this case it is possible to use the method of testing the hypothesis of equality of the mean values of a random variable.It is recommended to perform the hypothesis test on the homogeneity of two samples using the following method: the entire set of two samples is divided into intervals, then in two arrays, each sample is determined separately according to these intervals and the criterion for testing the hypothesis is calculated based on the dependence, which takes into account the volume of the first and second samples; the frequency in the interval for the first and second samples; the number of intervals for dividing the total sample. To test the hypothesis on the type of distribution, it is recommended to use the Kolmogorov criterion, the sequence of calculations when using this criterion is as follows: the sample is divided into intervals and the experimental accumulated frequency is determined; the theoretical accumulation of frequency is calculated based on the proposed type of distribution, the parameters of which are calculated from the initial data; the maximum difference between the accumulated theoretical and experimental frequencies in the corresponding interval is determined; the parameter Dmax= (mт- mе)/n is calculated, and then the criterion = Dmax √n. According to the corresponding tables for the criterion, the probability P(λ) that the hypothetical distribution function does not contradict the sample data is determined.
Keywords: forming tools; chromium-nickel cast iron; technological characteristics; operational characteristics; statistical research; random variables; correlation analysis