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The steady increase in the number of road users and their growing mobility mean that the issue of road safety is still a topical one. Analyses of factors influencing the number of road traffic accidents contribute to the improvement of road safety. Because changes in traffic volume follow a daily rhythm, hour of the day is an important factor affecting the number of crashes. The present article identifies selected mathematical models which can be used to describe the number of road traffic accidents as a function of the time of their occurrence during the day. The study of the seasonality of the number of accidents in particular hours was assessed. The distributions of the number of accidents in each hour were compared using the Kruskal-Wallis and Kolmogorov-Smirnov tests. Multidimensional scaling was used to present the found similarities and differences. Similar hours were grouped into clusters, which were used in further analysis to construct the ARMAXmodel and the Holt-Winters model. Finally, the predictive capabilities of each model were assessed.

Modelling the time that the system remains in a given state using classical distributions is not always possible. In many cases, empirical distributions are multimodal due to the influence of external, hidden factors and the selection of the best classical distributions may lead to erroneous results. In the article the method of diagnosis of influence of hidden factors into sojourn time of semi-Markov models was presented. In order to capture hidden factors, the authors proposed to model the distributions of the sojourn time with a mixture of distributions, which is a significant novelty in relation to the studies presented in the literature. Hidden factors directly affect the reliability of technical systems. Detecting the existence of these factors enables more accurate modeling of system readiness. Paying attention to irregularities caused by hidden factors makes it possible to reduce system maintenance costs. Such a system model provides complete information and enables a reliable assessment of the system readiness and maintenance. [ABSTRACT FROM AUTHOR]