Logical-probabilistic model for managing maintenance and repair processes of a shipbuilding company using copulas

Abstract

Purpose of research . The purpose of research is to develop and substantiate a logic-probabilistic model for managing maintenance and repair processes of ship technical systems, taking into account the stochastic dependence between component failures using copula theory. The study also aims to quantitatively assess the impact of external operational factors on equipment reliability and on the accuracy of critical failure prediction Methods . The study applies the logic-probabilistic reliability analysis method (fault tree analysis) to formalize the structure of a ship system and describe the conditions leading to a critical system failure. To model statistical dependence between failures of interconnected components, the Clayton copula is employed, enabling the representation of strong lower-tail dependence. Failure probabilities of individual components are determined based on the exponential time-to-failure distribution. A corrective function reflecting the impact of exogenous factors (humidity, salinity and vibrational load) is incorporated into the model. Empirical validation is performed using operational data from 15 vessels of Project 22870 for the period 2020-2024, applying absolute and relative error metrics. Results . The results show the accounting for the dependence between the cooling pump and the generator increases the estimate annual probability of a critical system failure from 28.11% to 37.04% (a 31.77% relative increase). The probability of their joint annual failure reaches 17.52%, which is more than twice the estimate obtained under the assumption of statistical independence. Model validation demonstrates a deviation of less than 2.88% from observed data. Conclusion . The proposed model provides a more accurate assessment of operational failure risks and can serve as a tool for adaptive maintenance planning, as well as integration with digital twins and predictive maintenance systems in the shipbuilding industry.