Semi-Markov model for the Kaplan preventive repair system for water turbines

Abstract

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.