Research on the causes of erroneous forecast generated using the Chapman-Kolmogorov equations for the process of vehicle operation

Abstract

The work attempts to investigate the causes of incorrect predictions of the Chapman-Kolmogorov system of equations generated during vehicle operation. When researching the process of exploitation of technical objects, Markov theory is often used in literature on the subject. Based on the developed Markov or semi-Markov models, on the one hand, basic reliability indicators (such as readiness) are assessed, and the evolution of the considered operation process is anticipated. The solutions of the Chapman-Kolmogorov system serve as the basis for preparing the forecast. For applications, forecasts of limit probabilities, determination times, and oscillation parameters of the probabilities of the states of the exploitation process are useful. The literature on the subject indicates the interdependence of each forecast on the estimation errors of all elements of the transition intensity matrix of the model, as well as errors in the calculation of its eigenvalues, as a potential cause of unsatisfactory forecast performance in continuous time. Considering the above, the main topic of this work was to investigate the correctness of the Chapman-Kolmogorov assumption for the vehicle operation process, the solution of which will make a significant substantive contribution to the current state of knowledge on modeling operation processes.