An Analytical Solution to the Problem of Summing Two Freight Flows Given by Triangular Distributions

Abstract

Transportation of the rock mass is often a limiting factor to increase the overall performance of a mine among other technological processes of a mining company. The study of the processes of formation and transformation of freight traffic will make it possible to clarify the methodology for designing continuous transport systems. The normative method of selection of the belt conveyors is based on the concept of freight traffic as normally distributed random variables, while point value - coefficient of irregularity - is the main indicator. There are doubts about the methodological justification of this approach. The normal distribution law in the classical version adequately describes a random variable varying in infinite limits, and the real mine freight traffic of conveyor lines are random variables with double restrictions. Most of the tasks of establishing the estimated ranges of freight traffic can be solved based on the use of experimentally established distribution functions (or probability density) of random values of freight traffic. Based on the recent publications, as well as our own experimental research, it is proposed to describe the freight traffic by piecewise linear functions of probability density, in particular, triangular, and to sum up the freight traffic based on the general theoretical provisions of the classical theory of probability. The article solves a particular problem of finding an analytical solution for the sum of two random freight traffic given by triangular distribution laws, providing a comparison with the result of numerical integration of the freight traffic.