SIMULATION MODEL OF THE ADAPTIVE MAINTENANCE PROCEDURE OF COMPLEX RADIOELECTRONIC FACILITIES

Context. The process of maintenance of modern radio-electronic facilities is aimed at supporting the serviceability or performance of the facilities during their technical operation. Specifications for achieving high reliability of operation are often contrary to other required characteristics, such as reducing the size of the product, obtaining high accuracy, reducing the cost of operation, etc. Therefore, the problem of the optimal choice of maintenance parameters to solve various tasks of operation using different criteria is relevant. Objective. The objective of this research is developing approaches to determine the optimal parameters of the process of adaptive maintenance. Method. Within the framework of the general simulation statistic model of the process of maintenance and repair of a complex facility (REF), we have developed a simulation model for parameter optimization of one of the maintenance strategies. The general simulation statistic model is intended to simulate the process of the TMR of the FEF in order to predict the reliability and value of the facility operation. Optimization of maintenance parameters improves both indicators of reliability of the facility and economic indicators of operation of the facility as a whole. The parameters are optimized on the basis of the criterion of a minimum specific cost of the REF operation or the criterion of the maximum ratio of technical use. In both cases, limitation means the required value of the mean time between failures of the facility, and as a method of optimization, we use the method of directed search within the scope of the maintenance parameters. An expert can participate in the process of finding an optimal solution, being involved in the analysis of intermediate data and making a decision on the completion of the search process. Results. The improved method of optimizing the maintenance parameters is a mathematical and algorithmic basis for the general software of the simulation statistic model of the maintenance and repair process. The method is programmed and tested in solving testing tasks. The results of the computational experiment are illustrated in the tabular form. Conclusions. In our work we have developed the simulation model of the process of adaptive maintenance of a complex radio-electronic facility. The model enables to substantially simplify and automate the process of research and optimization of the adaptive maintenance parameters of a complex radio-electronic facility. By adding the least reliable elements gradually to a plurality of items subject to servicing and modeling the random moments of the failure time, the simulation model calculates the optimal maintenance options with the adaptive time of condition monitoring. The simulation model is based on the algorithmic model and algorithmic optimization methods for adaptive maintenance, developed in our research, and works in the ISMPN software environment. As a method of optimization, we use the method of directed search within the scope of the maintenance parameters, with a DN distribution as a mathematical reliability model for electronic components and DM distribution for mechanical components. The practical value of the research lies in developing software which optimizes the maintenance parameters and predicts the reliability and value of operation for the given REF. The results obtained are to be used when determining the requirements for the parameters of operation of both new facilities and those of the available stock.


ABBREVIATIONS
ISMPN is a simulation statistic modeling program; АM is an adaptive maintenance; DB is a database; REF is a radio-electronic facilities; OTM is a operation time maintenance; OCM is an on-condition maintenance.  m E is a conditionally optimal set of elements maintained; ssa K is a steady state availability factor; is a function of the steady state availability factor with the optimal value of the maintenance level is an optimum, in the current step, value of the steady state availability factor; ) ( k t L is a smoothed value for current control time k t ; I N is a number of simulations implemented;  am P is a conditionally optimal parameters of adaptive maintenance;  am P is an optimal parameters of adaptive maintenance; U is a required vector of defining parameters levels, which determines the necessity for maintenance of elements;  m U is a conditionally optimal vector of defining parameters levels, which determines the necessity for maintenance of elements; is a conditionally optimal vector of defining pa-

INTRODUCTION
The task of providing the necessary indicators of reliability of complex REF arises very often, both in the design of new models of equipment (modernization) and in the operation of available ones. Complex radio-electronic facilities are recoverable facilities of long-term application. The cost of such facilities is high, as well as the costs of operation. Diversity and the stochastic nature of the impact of various operational factors on the radioelectronic facilities result in the fact that, with the same operation time or duration of operation, facilities, in terms of reliability, have different actual technical condition. Due to this fact, operation or calendar time does not expressly characterize the technical condition of the facility.
In order to provide the required level of reliability of REFs during their operation, maintenance and repairs are usually performed, the essence of which is to timely restore the operational condition of the facility and the preventive replacement of the items in the pre-failure condition.
On the one hand, a longer period of maintenance enables to increase the production operation of REF, as well as the operation profitability. But this is not the case with the use of an outdated equipment stock which significantly increases the time of maintenance due to the elimination of intensively increasing failures and malfunctions.
The object of study is the maintenance process of complex radio-electronic facilities.
The subject of study is optimizing the parameters of adaptive maintenance.
The purpose of the work is to develop approaches to determining the optimal parameters of the process of adaptive maintenance.

PROBLEM STATEMENT
Depending on the criterion used in determination of the timing of maintenance, there are two main strategies for arranging maintenance: OTM and OCM. When performing OTM, control is exercised according to the available potential of the facility, and when the residual life reduces to some predetermined threshold, the facility maintenance is performed. When conducting OCM, the current technical condition of the facility is monitored, with maintenance performed, if the technical condition of the facility deteriorates to some predetermined unacceptable threshold. In turn, two types of strategies can be identified during OCM: OCM with a constant control period and OCM with a variable control period (adaptive OCM).
Each strategy is characterized by its parameters, which can be simulated using simulation statistic modeling. The modeling criteria of determining parameters of adaptive maintenance in our research are as follows: the criterion for minimizing the specific cost of the facility operation, which is determined at a reference period of operation, with the provision of a reference requirement to the reliability level of the facility, and the criterion of maximizing the coefficient of technical operation with the provision of the same requirement to the reliability level of the facility [1][2][3][4].
To perform modeling, it is necessary to create simulation models for all maintenance strategies.
The initial data for ISM are the following variables: . The limitation is the use of DN distribution, as a mathematical model of reliability of electronic components and DM distribution, for mechanical components.

REVIEW OF THE LITERATURE
Nowadays, many scientists also investigate the problem of optimizing the maintenance process for different types of facilities. Thus, to minimize the cost of servicing systems with the reliability constraint, work [5] suggests the approach which uses the methods of Lagrangian relaxation embedded in dynamic programming. The approach can be applied to determined and probable tasks of dynamic programming, as well as to Markov partially observable decision making process. The computational complexity of the approach is polynomial with regard to the number of Q-components of the system. The author of work [6] addresses the problem of optimizing maintenance in a multi-component system which performs several missions with scheduled finite discontinuity. Due to the limited time, budget, or availability of resources, maintenance can only be performed on a limited set of components. To do this, we propose a new integrated formulation of nonlinear programming for the sample maintenance, which enables to choose the components to be serviced, the maintenance levels to be performed, and maintenance tasks for several maintenance technicians. In work [7], a stochastic optimization model is considered to reduce the long-term total cost of maintenance complex systems. The work relies on the following principle: optimization of cost models for complex multi-component systems is based on analyzing the reliability of different maintenance approaches (regular block and age ones) and on clustering maintenance actions to reduce the total cost of maintenance of a complex system. In work [8], in accordance with the task of optimizing maintenance, the author selected the most important components of the power system with renewable energy sources. Then a set of maintenance strategies is proposed for all critical components. The total cost of each strategy for all critical components is calculated as the amount of costs for: operation, maintenance and environmental protection. The best maintenance strategy for each critical component is selected by identifying the lowest total cost of different maintenance strategies.
The author of work [9] addresses a new method of optimal strategy of maintenance of a complex system taking into account the reference reliability limitation. It is based on the direct analysis method which provides accurate quantitative determination of the reliability of highly reliable maintenance systems. As a discrete maintenance model, the article considers a model where each maintained component can operate in one or more discrete maintenance modes. In work [10] the author considers the optimal schedule of preventive maintenance of one element on the finite segment on the basis of Bayesian models of the failure function. In work [11] a new approach to the modeling of maintenance of machine tools is developed taking into account the architecture of stock systems. The stock architecture is considered, which consists of various types of machine tools of different manufacturers of equipment, working with different users, but supported by one repair shop. The essence of the approach is to jointly optimize the decisions on the levels of repairs, namely: the schedule of repair, relocation, disposal and preventive maintenance, taking into account the structure of user costs and policy in the workshops. In work [12], the author suggests a new approach to cost-effective optimization of maintenance completion strategies for a set of repaired elements. The optimization method consists of two stages. Firstly, a new concept of matrix modeling is introduced to find the scope for solving this optimization problem. Secondly, a genetic algorithm is used to find a solution with minimal costs. It is shown that the combination of matrix modeling and genetic algorithm is a powerful method for solving the problem of optimization. In work [13], the MINLP model is suggested which represents a stochastic process of failures and repairs of the system in the form of a Markov continuous-time chain, on the basis of which the choice of backup and frequency of verification and maintenance tasks is optimized for maximum profit. The model explicitly takes into account all possible conditions of the system. It also offers effective decomposition methods and reduction of maintenance scenarios.
Thus, the task of developing simulation models and improving the procedure of optimizing the adaptive oncondition maintenance parameters for two different criteria is relevant.

MATERIALS AND METHODS
The development of a simulation model for optimizing the parameters of the process of adaptive maintenance should be based on a pre-formalized adaptive maintenance model. In our work we use an improved model as the formalized model of adaptive maintenance, which is described in works [1]. The optimization task was solved for one of two criteria: optimization by criterion e c min (1) and by criterion Constants of smoothing are not directly related to the choice of maintenance options. For this reason, the parameters    , , are not included in the number of optimized strategy parameters, and we regard them as constants.
When solving a problem (1) the set m E is fixed, with the sequence of partial problems solved. At each step, an auxiliary set  m E is formed by adding one element from the set m E , with a specific task solved for determining the optimal parameters satisfying the condition: is met in a certain step, the process of search for a conditionally optimal solution is completed. This solution, obtained in the final stage, is taken as the general optimal one * P a m . Figure 1 shows the algorithmic model of the task solution (1  depending on the value of the lead ratio  , which binds the scheduled time interval to the next maintenance ) ( k m t T , with the current predicted value of the mean time between failures of the least reliable element ) ( k ср t T  : For a two-parameter exponential smoothing model, estimation of the average degradation rate of the i-th element is determined by the expression: . DOI 10.15588/1607-3274-2020-1-7 For a three-parameter smoothing model [14,15]: determines the dependence of the optimal maintenance level of the i-th element on the ratio  .
The value ) ( is the specific cost of operation obtained with the optimum value of the maintenance level Statement 6 determines the optimal value of the ratio   in the current step, which satisfies the condition: Statement 7 determines the optimum value of the maintenance level: is constructed, with the optimal value determined in Statement 5 on the basis of the condition: The content of all other operators remains unchanged. Taking into account the aforementioned, one can formulate the following method of optimizing the parameters of the adaptive maintenance process of a complex radioelectronic facility: 1. Create a database of the REF, with the task of optimizing the adaptive maintenance parameters solved.
2. Specify the simulation parameters for ISMPN. . Determine the conditionally optimal maintenance parameters for one maintained element. 5. Determine the mean time between failures and compare with the required one. If the mean time between failures is less than required, add the second one, etc. to the list of maintained items, till the mean time between failures is no less than necessary.
6. Determine the optimal parameters of adaptive maintenance.

EXPERIMENTS
The problem is solved using the ISMPN program. In each step of the task solving, actions are performed in accordance with the following procedure:   , we determine the optimal value of the maintenance level for element As a result of the calculations performed in step 1, we obtain the following conventionally optimal solution: 3. According to the chart ) ( 0   T , we determine the mean time between failures  0 T = 1.386 hours, which is achieved with these parameters (shown next to the chart on the right).

If the requirement
is not fulfilled, we take the next step. But before proceeding to the next step, we enter the latest value of the maintenance level   1 m u (for element 132) in the database.
The final modeling results are shown in Table 2.
To ensure the reliability level req T 0 = 1.500 h, the parameters obtained in step 2:  The statistical error of the modeling results, with the above results obtained, is 148 . 0   . Optimization by criterion ssa K max .
1. In step 1, we add element 132 to the set  m E : 2. We launch the ISMPN program in the mode "Optimizing maintenance/adaptive maintenance" and specify the following variation parameters: -for m u :  does not have a stable maximum, so we immediately proceed to step 2 and add element 12 to the set Figure 3 shows the view of the PC screen after completing the simulation in Step 2.
In step 2, the maximum of the function ) (  ssa K is obtained at the value of the argument   = 0.65. According to the chart, we find conditionally optimal value of the maintenance level ) ( = 0.65. All these data are calculated in a programmatic manner and displayed to the right of the corresponding chart. Thus, after completing step 2, we obtained a conventionally optimal solution: . Table 4 shows the compared parameters.
The  The obtained results adequately demonstrate the peculiarities of the simulation model of optimizing the parameters of the adaptive maintenance strategy, as well as the possibility of application of the modeling results obtained.

CONCLUSIONS
The simulation model of the process of adaptive maintenance of a complex radio-electronic facility is developed in the work. The essence of the simulation model is that by gradually adding the least reliable elements to a set of elements to be maintained, and simulating random moments of the failure time of the facility elements, the model calculates the optimal parameters of maintenance with the adaptive time of the technical condition control.
The scientific novelty of the research is to improve the simulation model of the process of adaptive maintenance of a complex radio-electronic facility, which, unlike available ones, is based on the algorithmic model and algorithmic optimization techniques used in the software package of the ISMPN. As a method of optimization, we use the method of directed search within the scope of the maintenance parameters; as a mathematical model of reliability, we use the DN distribution for electronic components, and DM distribution for mechanical components, with the scheduled time interval to the next maintenance determined on the basis of the threeparameter exponential smoothing model, which enables to significantly simplify and automate the process of studying the reliability of indicators and optimization of adaptive maintenance parameters of a complex radioelectronic facility. The practical value of the results obtained lies in developing software which optimizes the maintenance parameters and predicts reliability indicators and operation cost for the given REF. The results obtained are to be used when determining the requirements for the parameters of operation of both new facilities and those of the available stock.
Prospects for further research lie in creating simulation models and software tools for optimizing the parameters of the process of scheduled maintenance of REFs, maintenance and repair procedures of the REF groups.