CHOOSING THE SYSTEM OF LOCOMOTIVE MAINTENANCE IN VIEW OF THE EFFECT OF DEPENDENT FAILURES

Dep. «Locomotives», Dnipropetrovsk National University named after Academician V. Lazaryan, Lazaryan St., 2, Dnipro, Ukraine, 49010, tel. + 38 (056) 733 19 01, e-mail bodnarz@nz.diit.edu.ua, ORCID 0000-0002-3591-4772 Dep. «Locomotives», Dnipropetrovsk National University named after Academician V. Lazaryan, Lazaryan St., 2, Dnipro, Ukraine, 49010, tel. + 38 (056) 733 19 61, e-mail abochkasov@gmail.com, ORCID 0000-0002-7719-7214 Dep. «Higher Mathematics», Dnipropetrovsk National University named after Academician V. Lazaryan, Lazaryan St., 2, Dnipro, Ukraine, 49010, tel. +38 (0562) 36 26 04, e-mail grishechkina.tatiana@gmail.com, ORCID 0000-0003-1570-4150 Dep. «Locomotives», Dnipropetrovsk National University named after Academician V. Lazaryan, Lazaryan St., 2, Dnipro, Ukraine, 49010, tel. + 38 (056) 733 19 61, e-mail Melnar78@gmail.com, ORCID 0000-0001-6040-913X


Introduction
The task of minimizing total costs at all stages of the lifecycle of vehicles, improving the reliability and safety of equipment is common to both locomotive developers and operating transport com-panies. For the rail industry, minimizing such costs increases the competitiveness of products and, consequently, stimulates the expansion of the market and increase in profits. For operating companies, thus, the economic efficiency of using rolling stock rises [10].
When substantiating the choice of the most advantageous offer for the supply of traction rolling stock, transport companies, along with comparison of technical characteristics, are increasingly using the LCC (Life Cycle Cost) indicator. Величина капітальних затрат на придбання нового тягового рухомого складу поступово починає замінюватись величиною витрат на всіх етапах життєвого циклу локомотива The amount of capital costs for the acquisition of a new traction rolling stock gradually begins to be replaced by the cost of all stages of the locomotive life cycle [14,17,18].
Actuality of LCC approaches in locomotive services is explained by the introduction of new locomotives with onboard control and diagnostic systems, as well as the development of the theory of traction rolling stock maintenance systems. The cost of a locomotive as a traction unit ceases to be the determining factor. This is due to the fact that maintenance and repair costs for the entire life cycle of a locomotive considerably exceed its initial cost.
The works [3, 5, 9, 11-13, 15, 16, 21] are devoted to the introduction of LCC approaches at the stages of selecting, updating, modernizing and operating the traction rolling stock. Despite a significant number of research results on the use of LCC indicators, the issue of assessing the degree of influence of reliability indicators of locomotive assemblies on the choice of the maintenance system and the cost of the locomotive life cycle remains unsolved.

Purpose
The main purpose of the work is to increase the efficiency of the use of locomotives by choosing a rational maintenance system that takes into account the assessment of the effect of dependent failures on the cost of their life cycle. To achieve this purpose, it is necessary to analyze the existing approaches for managing the locomotive life cycle cost, as well as to develop a method for assessing the degree of influence of reliability indicators of locomotive nodes on the choice of the maintenance system and the cost of the locomotive life cycle.

Methodology
The most commonly used approach in developing life-cycle cost management systems is the RAMS (Reliability, Availability, Maintainability, Safety).
Let us consider its embodiment in the railway standards of Europe, Russia and Ukraine.
The main characteristics, definitions and terms relating to RAMS and LCC of rail transport facilities are given in European Standard NF EN 50126-1-2000 [20]. An example of the practical use of the RAMS approach for assessing the safety status of locomotive facilities using an integral indicator is described in [19].
The basic provisions of the RAMS can be used to assess the locomotive operation and maintenance system in terms of reliability, availability, maintainability and safety during their interaction. The proposed approach defines the process based on the life cycle of the whole system, and the tasks in it; allows to effectively monitor and control the interaction between the elements.
Standard EN 50126 [20] presents the system (locomotive) life cycle that is a sequence of phases, each of which solves the corresponding tasks, which cover the entire system service life from the original concept to decommissioning.
The life cycle provides a framework for planning, managing, controlling and monitoring all aspects of the system, including RAMS. Fig. 1 shows the life cycle stages according to this standard.
At each stage of the life cycle, there are certain, related to this stage, tasks: general, tasks of reliability, performance, repairability, as well as also safety-related tasks.
The issues concerning calculations of the system life cycle cost are considered in the second stage, while forming the profile of the system purpose. The costs incurred during the design phase of the system, as well as those planned during the formation of the requirements for operation and maintenance, constitute a significant part of the locomotive life cycle cost.
It is impossible to determine the exact costs for the entire life cycle. They can be evaluated only with different degree of confidence.
Initial data for the analysis and calculation of the life cycle cost of the traction rolling stock are: 1. During the reliability, availability, maintainability and safety analysis (RAMS analysis): -Service life; -Average annual mileage of the locomotive; -Average time of locomotive operation per year; -Other quantitative and qualitative indicators of the use of locomotives.
2. When determining the life cycle cost (LCC analysis): -Specifications / technical manuals from the component or subsystem provider (for example, FIT rate, MTBF rate) -Identification, collection and use of statistical data (for example, failure rates, repair costs, part replacement statistics, part wear dynamics, etc.); -Models for forecasting changes in the technical condition of the locomotive and its subsystems; Databases and statistical reports on the reliability and operation of locomotives.
The [20] presents two methods for calculation of costs for the life cycle components: -Calculation of costs for preventive maintenance (analogue of planned preventive repair system); -Calculation of costs for corrective maintenance (after failures) (analogue of the current state maintenance system).
Let us consider these methods in more detail. Calculation of costs for preventive maintenance. Preventive maintenance, in accordance with European Standard EN 13306 (2001) [8], is maintenance performed at specified intervals or according to the proposed criteria. It is intended to reduce the likelihood of a failure or deterioration of the functioning of the technical unit.
Calculation of costs CY_MP for preventive maintenance during a life cycle is carried out by the formula: for organizational, administrative and logistic processes; for purchase / delivery of consumables; for emptying of wastewater reservoirs; in anticipation of service; for utilization duration; for external and internal cleaning of the vehicle.
Calculation of costs for corrective maintenance. Corrective (unscheduled) service according to [20] is the maintenance performed after the fault recognition. It is designed to restore a locomotive to a technical state in which it can perform the necessary functions.
Calculation of costs for corrective maintenance CY_MC during the life cycle is performed according to the formula: where Basic rules for determining the cost of life cycle of rolling stock and complex technical systems of rail transport on the Russian railways are given in [11]. This method contains the main provisions and formulas for calculating such indicators of the efficiency of rolling stock and complex technical systems of rail transport, as the life cycle cost, the useful economic effect and the limit price of machinery.
The life cycle cost indicator is used in this methodology to evaluate the effectiveness of innovative measures, including those at rail transport.
The term «Life cycle cost» (LCC) of the technical equipment in [11] is defined as the total consumer's cost for the purchase and use of the equipment for the duration of its service.
The life cycle costs of the technical equipment include all consumer costs associated with its acquisition and possession, that is, the purchase price, the associated one-time costs, as well as the operating costs for the entire life and the costs of disposal.
The [11] proposes to limit the number of life cycle stages of technical equipment by the following stages: 1) Development of concepts and definitions; 2) Research and development works; 3) Manufacturing of technical means; 4) Putting technical equipment into operation with accompanying measures to train the personnel, upgrade the repair base, etc.; 5) Operation and maintenance; 6) Retirement (liquidation, disposal). The general LCC of a product (of all its six stages) is divided into two main parts: 1) Costs associated with the acquisition (stages 1-4); Costs related to operation and disposal (stages 5-6).
Initial LCC analysis is carried out at the acquisition stagecomparisons are made with analogues. Then, during the exploitation phase, the monitoring of economic indicators is carried out in order to confirm the initial life cycle costing.
LCC of rolling stock and complex technical systems of rail transport is defined in [11] by the formula: where Pacqobject acquisition price (initial value the equipment acquisition price can be presented as its limit price; Otannual operating costs; t К  accompanying one-time costs associated with putting of machinery into operation; t Ddisposal value of the object; t discount coefficient; tcurrent year of operation; Тfinal year of operation, established in accordance with the technical requirements or other documentation (including the accounting policy of the enterprise on whose balance the object is located).
The discount coefficient for the constant discount rate is determined by the expression: where tstep of the calculation period (t = 0, 1, 2, ... Т); Тtime horizon (life cycle duration); Еdiscount rate.
In [13] it was noted that despite the significant number of research results regarding the use of the LCC economic indicator as one of the main criteria for evaluating and approving investment decisions in the long run, the issue of adaptation of this indicator to the operational features of Ukrainian railways needs further development. The paper proposes to calculate the rolling stock life cycle cost for alternate investment variants in its renewal as follows:

Findings
The conducted analysis of the life cycle costing approaches allows us to conclude that none of the considered methods takes into account the effect of failure of one node on the failure of other connected nodes (dependent failures of system elements) of the locomotive. According to researches [4,6], quite a significant part of failures (and, as a consequence, of unscheduled repairs) occurs due to the dependent failures of elements. Thus, when calculating LCC and costs for all types of maintenance, it is necessary to take into account the effect of dependent locomotive failures.
One of the LCC components is the locomotive maintenance cost. The amount of these costs depends on the reliability indicators and the accepted technical maintenance system. Methods for assessing the economic efficiency of a locomotive maintenance system are given in [2,3,7]. In order to improve the methodology for calculating the locomotive maintenance system cost, the authors національного університету залізничного транспорту, 2018, № 6 (78) suggest taking into account the dependent failures of nodes. According to [3], the cost of unscheduled repairs in a rational system without taking into account dependent failures can be defined as follows: In order to calculate the renewal costs during unscheduled repairs, it is necessary to take into account dependent failures of the elements. To cal-culate the life cycle cost of a locomotive with account taken of the dependent failures of its elements, it is necessary to determine the probabilistic dependencies between the failures of its main nodes, that is, with what probability the failure of each node will affect the failure of other locomotive nodes.
The average cost of one unscheduled repair з C , taking into account the dependent failures, is determined by the expression: where і sch Ccost of one scheduled repair of the ith dependent element; i pprobability of dependent failure of the i-th element; Vset of dependent elements.
Calculation of the probability of dependent failures can be performed using expert research methods [1], methods of fuzzy logic and neural networks [22]. In general, the probability of occurrence of dependent failures is presented in the Table 1. Table 1 Probabilities of occurrence of dependent failures Table 1 in the columns indicates the names of nodes with primary failures, and in rowsthe names of nodes with dependent failures. The elements of this matrix (tables) are filled by experts, which indicate the probability of dependent failures for each node of the locomotive.
For example: p12 is the probability that a dependent failure of Node 1 will occur in the event of Node 2 failure. In general: pіNprobability that a dependent failure of the Node i will occur in the event of the Node N failure.
It is obvious that the probabilities of the type are always equal to one.
To estimate the influence of dependent failures on the locomotive maintenance system and life cycle cost, we propose to use a coefficient df P .

Originality and practical value
For the first time, it is proposed to use the concept of the effect of dependent failures to calculate the locomotive renewal cost when performing unscheduled repairs, as well as the locomotive life cycle cost.
The method of determining the unscheduled repair costs with consideration of dependent failures was improved in the work; and the coefficient of assessing the effect of node dependent failure on the locomotive maintenance system was introduced.
The calculation method can be used to compare and evaluate variants of the locomotive maintenance system and to develop systems for their diagnosis.

Conclusions
The work analyzed the existing approaches to the management of the life cycle cost of locomotives at the stages of their selection, renewal, modernization and operation.
We substantiated the necessity of improving the methods for assessing the degree of effect of reliability indicators of locomotive units on the choice of the maintenance system and its life cycle cost.
We conducted the analysis of modern approaches to managing the locomotive maintenance system.
It is proposed to use the concept of «effect of dependent failures» when calculating the locomotive renewal cost after unscheduled repairs and the locomotive life cycle cost.
The proposed coefficient of the effect of the node dependent failure on the locomotive maintenance system will allow determining the nodes, the failure of which affects the renewal cost more than their nominal value. Also, this coefficient will help to take into account probable losses due to node failure during the development and adjustment of the locomotive maintenance system. національного університету залізничного транспорту, 2018, № 6 (78)