Probabilistic Modeling of the Duration of Repair and Reservation of Passenger Cars

The problem that the paper is devoted is to construct statistical density functions for the time indicators under study, to select approximating dependencies, and to verify whether the repair duration complies with an exponential distribution law. Research methods: statistical processing of a database of operational data containing information on 100 passenger cars of 47D/k model; interval grouping; construction of a statistical density; the least squares method; the coefficient of determination; Pearson's chi-squared test. The novelty of the work is in the joint probabilistic study of the duration of repair and reservation of a homogeneous sample of passenger cars, as well as in distinguishing between the calendar time a car spends in a repair state and the time spent directly performing repair operations. The study results show that the duration of repair of passenger cars can be described by an exponential distribution with a parameter λ ≈ 0.016 day⁻¹. The average value is about 63 days. The exponential approximation using the least squares method is characterized by the coefficient of determination R² = 0.9659. After combining intervals with low theoretical frequencies, the calculated value of Pearson test is χ² = 2.05, which does not provide grounds to reject the selected model at a significance level of 0.05. The average duration of reservation is about 186 days; no correspondence is found with any of the considered classical distribution laws. Conclusions: the obtained dependencies can be used for probabilistic assessment of the duration of removing cars from service and for identifying ways to reduce organizational and logistical delays.