THEORETICAL STUDIES ON THE PROCESS OF CHANGE OF THE TECHNICAL CONDITION OF FREIGHT CARS IN OPERATION

Purpose. The scientific work is intended to investigate the technical condition of freight cars during their operation. The said purpose involves solving the following tasks: 1) to describe the technical condition of a freight car during the maintenance and repair period; 2) to determine the dependences of the probability of a freight car being in working condition during the life cycle; 3) to specify the expression for the technical availability ratio of the car fleet. Methodology. To achieve the purpose, the author examined the methodological approaches to the definition of various stages of the freight car life cycle. The system of change and transition of the technical condition of the freight car is described using differential equations. Findings. In the case of an unstable process of changing the technical condition of a freight car, the probabilistic characteristic of the appropriate life cycle stage depends on the amount of time. The intensity of the input and output flows are correlated with each other, taking into account the probability of a freight car being at the appropriate stage of its life cycle. Originality. Transitions from one car life cycle to another occur in discrete steps, that is, such transitions are characterized by a random process. The probability of a freight car being at the appropriate life cycle is determined by its prior technical condition. The total value of the set of all possible conditions consists of the Markov chain for random processes with random states and a continuous flow of time. The study resulted in obtaining, for the first time, of the dependence of the probability of a freight car being in working condition during the life cycle. Practical value. On the basis of the obtained definition for the probability of the freight car being in working condition the expression for the technical availability ratio of the car fleet was clarified.


Introduction
The main task of rail transport is to ensure uninterrupted transportation process, the mandatory condition of which is the safe railway operation [9,17]. Successful implementation of the tasks facing the railway needs to improve the technical level of rolling stock, the introduction of modern highefficient constructive solutions, materials and technologies [12,16,18,19]. In order to maintain a high technical level of the car fleet, it is necessary to introduce the modern technologies for renewal and increase of wear resistance of parts, improvement of the maintenance system of cars in operation [4,8,10,13,15]. With the introduction of new information technologies that enable the automatic identification of cars and their individual parts, even the normal operation of the car can be viewed as a stand for reliability testing [6,11]. The analysis of publications on this problem indicates the need for theoretical studies of the process of changing the technical condition of freight cars in operation [1,7,14].

Purpose
The main purpose of the work is to investigate the process of changing the technical condition of freight cars in operation. To achieve it, it is necessary: 1) to describe the technical condition of the freight car during maintenance and repair; 2) to determine the dependences of the probability of a freight car being in working condition during the life cycle; 3) to specify the expression for the technical availability ratio of the car fleet.

Methodology
The freight car during its lifetime may be at different stages of the life cycle: in the initial state (test sample, which undergoes acceptance tests and has a trial run); on storage; in a good non-working condition (idle).
Transitions from one life cycle to another occur in discrete steps, that is, such transitions are characterized by a random process [2]. The probability of a freight car being at the appropriate life cycle is determined by its prior technical condition. The total value of the set of all possible conditions con-sists of the Markov chain for random processes with random states and a continuous flow of time. In this case, there is a sequence of dependent technical states [3]. The transition itself from one technical states n S to other k S occurs through the actions of the corresponding streams of events. Such events are failure or restoration.
Let us denote the failure flow intensity rate as  , and the restoration flow intensity rate of the technical condition of the freight car as  .
Characteristics of the corresponding technical condition of the freight car at a certain stage of the life cycle are given in Table 1.
T ab le 1

Stage of the relevant life cycle
Designation of technical condition, S Failure intensity value, λ Restoration intensity rate of the technical condition, μ For the given technical conditions of the life cycle of a freight car it is possible to propose a marked diagram with corresponding transitions (Fig. 1).
The indication of the technical condition of the freight car is given in the circles, and the transitions themselves from one condition to another are indicated by arrows specifying the intensity of the failure or restoration flows. Each technical condition of the freight car is characterized by the corresponding probability: о Рprobability rate of freight car being in its original condition (a test specimen undergoing acceptance tests and having a trial run); -

Findings
In the case of an unstable process of changing the technical condition of a freight car, the probabilistic characteristic of the appropriate life cycle stage depends on the amount of time, while the intensity of the input and output flows are correlat-ed with each other, taking into account the probability of a freight car being at the appropriate stage of its life cycle.
The very system of change and transition of the technical condition of the freight car according to the diagram (Fig. 1) can be described by means of differential equations [3,5] For the probability of freight car being in working condition, we use the following differential equation: If we solve the system of equations (1-11), we can find the probability of the freight car being in working condition (12): t Р t о о о con con con con or con con or or or Р t t t con con or or or or Using the expression to find the probability of the freight car being in the working condition (12) where mthe number of freight cars in good technical condition; ithe corresponding freight car; tot mtotal number of the car fleet units.

Originality and practical value
Having formed the Markov chain for random processes of probability of the freight car being at a corresponding life cycle with random conditions and continuous flow of time, we for the first time obtained dependence of probability of the freight car being in the working condition during the life cycle. On the basis of the obtained definition for the probability of the freight car being in working condition the expression for the technical availability ratio of the car fleet was clarified.

Conclusions
The work considered change of technical condition of freight cars in operation occurs during the whole lifetime, and the technical condition can be in different stages of the life cycle. Transitions from one car life cycle to another occur in discrete steps, that is, such transitions are characterized by a random process.