Semi-Markov modeling for assessing reliability of road construction machines in the process of their operation

Abstract

The article provides a theoretical description of the processes of changing the technical state of road-building machines to assess their reliability at the stage of operation based on semi-Markov models. Reliability is the most important property of machines and characterizes their ability to perform their functions during normal operation. Reliability covers all stages of the life cycle of equipment-its design, manufacture, and operation. The operation stage is the longest in time and the costliest to ensure reliability. This explains the relevance of developing a mathematical model of operational reliability of road-building machines. During the operation of technical objects, their technical condition changes under the influence of objective and subjective factors. As a result, quantitative indicators that characterize the technical condition of machines vary widely and are random in nature. Road-building machines may be in one of the following technical states during operation: perfect, imperfect, upstate, down state. At the same time, a perfect machine is always upstate, and an imperfect one can be either upstate or down state. The transition from one technical state to another is random and can be considered instantaneous with a sufficient degree of accuracy. The probability of any technical state in the future depends only on the state of the process in the present and does not depend on when and how the process was in this state. This makes it possible to use the theory of semi-Markov processes when formalizing the process and developing a mathematical model. Based on semi-Markov modeling, the article shows the sequence of constructing a graph of states and transitions from one state to another for a road construction machine during operation; matrices of transitions and probabilities of transitions from one state to another; systems of differential equations for determining the limiting probabilities of finding a machine in a particular technical state during operation. The developed method of semi-Markov modeling allows estimating the operational reliability of equipment with the reliability allowed by probability theory.