Mathematical Modeling of Operational Reliability of Mine Lifting Equipment Based on Censored Data

In this study, a comprehensive mathematical method for modeling the operational reliability of mine hoisting equipment under conditions of incomplete and heavily censored data is developed. The analyzed dataset includes 259 observations collected over a five-year period for six critical components, with the overall level of censoring reaching 62% and exceeding 70% for long life mechanical subsystems. Considering right, left, and interval censoring, the paper proposes a unified statistical procedure that combines empirical estimation of failure rates with parametric identification using Weibull, exponential, normal, and lognormal distributions. Model parameters are estimated using censored data–aware fitting procedures, while model selection is performed based on likelihood-based criteria, supplemented by correlation analysis to assess agreement between empirical and fitted reliability curves. The methodology is implemented computationally in the Mathcad Prime environment and is supplemented with mathematical tools for reconstructing survival curves, analyzing parameter sensitivity, and evaluating robustness at different censoring levels. In addition, an economic optimization model is formulated to determine cost-effective maintenance intervals by minimizing an integral functional that accounts for preventive maintenance, repair, and downtime costs. The results demonstrate that the proposed approach provides stable reliability estimates and reliable forecast intervals, enabling the construction of generalized life cycle curves for individual subsystems. The study establishes a rigorous mathematical basis for the transition from fixed-interval maintenance to adaptive, reliability-oriented maintenance strategies in industrial mine hoisting systems.