The article presents a semi-Markovian model of a system of preventive repairs according to age, carried out in water power plants with the use of Kaplan turbines. In the case of the analyzed technical objects, the profit per unit of time is considered as a criterion for the considered function. On the basis of the adopted assumptions, formulas describing the criterion function were presented for the developed mathematical model, and then the conditions for the existence of the maximum of this function were formulated. The proposed method makes it possible to determine the optimal time for preventive repair of the water power plant under consideration. Theoretical considerations presented in the article are presented on the basis of a calculation example developed on the basis of estimated data obtained from a real Kaplan water turbine operation system.
In the article, there is presented the description of the algorithm of the operating process of the simulation model characteristics’ determination realized in the transport system. The simulation model of the means of transport’s operating process has been developed based on the that process’s mathematical model (semi-Markov model). Due of the assumed principles, the constructed model can be applied for the purposes of assessment and control of the operating process because of criterion of different types. Analysis of performance’s assessment of the operating means of transport is one of the ways of the possibilities of correct realization of the assigned transportation tasks in the transport systems. The simulation model of the operating process presented in the work, makes it possible to assess performance of the transport system’s operation from the point of view of the selected assessment criteria: availability of the means of transport and the unit income generated in the process’s modelling conditions. Based on the results of the tests conducted in the real system of the means of transport operating system, the model’s input data have been developed and simulation experiments have been conducted. As an effect, there have been determined the exemplary values of the analyzed characteristics of the transport system’s operation performance analyses.
The paper presents a semi-Markow model of a preventive repair system by age, implemented in hydroelectric power plants with Kaplan turbines. In the case of the analyzed technical objects, the profit per time unit is considered as the criterion of the quality of functioning. On the basis of the adopted assumptions, for the developed mathematical model, formulas describing the criterion function were determined and the conditions for the existence of the extreme (maximum) of this function were formulated. The proposed method makes it possible to determine the optimal time for preventive repair of the considered technical objects. The theoretical considerations presented in the work are illustrated by a computational example developed on the basis of data obtained from the actual operating system of Kaplan water turbines with a rated power of 120 kW.
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