Semi-Markov model for the Kaplan preventive repair system for water turbines with periodic inspection of the technical condition

Abstract

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.