Development of a mathematical model of the reliability of multifunctional transportation delivery systems

Abstract

A mathematical model of the reliability of multi-functional transport delivery systems was built in the form of a system of equations of the functions performed by the system and the total duration of their operation. A system of equations describing the principle of calculating the reliability of the multi-functional transport system as a participant in the process of transportation of goods and passengers is given and the main and reserve, active and passive functions of its work are highlighted, the total number of which may exceed the number of tasks it solves in a given period of time. An analysis of the specified functions is given, the total number of which is performed by a multifunctional system may exceed the number of tasks solved by it in a given period of time, and the opposite situation is also possible. It was found that when considering the duration of the transport system for each performed function, it is not important to know the periodicity of receipt and the number of solved tasks per unit of time, and therefore the uncertainty of this information does not reduce the reliability of the reliability assessment method for functional redundancy.

The probability of the system being in different states is given, an example of a state graph is given, and possible two-way transitions between elements are shown. Equations of the probability of activation of the functions of dual-functional transport systems are obtained and their schematic representation is given. An assumption is made regarding the possible re-activation of the same function, due to the emergence of tasks before the dual-functional transport system and their solution in an arbitrary order. It was revealed that the structure of the system is formed by two modules for the implementation of the necessary functions and a switch designed to activate the necessary function, its possible failures are described.

Expressions for evaluating the elements of the matrix of serviceable states of transport systems are presented. Emphasis is placed on the need to develop the desired mathematical model, not on probability, but on the statistical interpretation of determining the average duration of a specific function for a specific period of time.