" Estimation of efficiency of automobile transport systems on the basis of mathematical methods

Abstract

Logical-probabilistic methods of Boolean algebra allow not only to quantify the reliability of complex transport systems, but also to determine the role of individual elements of the structural scheme of reliability and their combinations in ensuring the reliability of road transport systems.

In the absence of information on the reliability of the elements, their impact on the reliability of the entire system is assessed using the concept of the weight of the elements in the structural diagram of the reliability of the transport system. The weight of the element characterizes the relative number of such critical working states of transport systems, in which the failure of the element leads to the failure of the system and vice versa, the restoration of the element leads to the restoration of the transport system of all its states.

It is shown how the elements of Boolean algebra can be used in assessing the reliability of the chains of elements of transport systems in general and how with the help of Boolean algebra concepts logical functions can be reduced to an orthogonal disjunctive normal form. An equivalent form of a logical function is given through elementary conjunctions of different ranks. It is shown how it is possible to use transformation of logical function in calculation of probabilities of faultless work of transport system. Logical functions are represented through elementary conjunctions as well as in matrix form. Transformations of a logical function are considered on the example of a transport system consisting of eight elements. The formula for calculating the probability of failure-free operation of such a transport system is obtained.

Concepts such as the assessment of the weight, significance and contribution of individual elements of the structural scheme of reliability in the reliability of the road transport system or its chain are clarified. The general formulas of probability of trouble-free operation (n-elements) for the transport system are obtained and their implementation is considered on the example of a structural scheme of five elements. The content of the probability of a monotonic logistic function and its derivative is considered. The formulas for calculating these characteristics for the system element are obtained. There are five important consequences of their relationship, taking into account the working and inoperable element in the structural scheme of reliability of transport systems.

Key words: estimation, working capacity, reliability, automobile transport system, elements, structural scheme, mathematical methods.