Integrated Approach to Modelling the Reliability of Gears in Ship Propulsion Systems

The operational reliability of gears in ship propulsion systems is an important factor affecting safety, efficiency, and cost-effectiveness in ship operation. Gear failures may result in loss of propulsion, increased maintenance costs, and risks to crew safety. This paper presents an integrated methodological framework for assessing gear reliability in ship propulsion systems by integrating qualitative causal analysis, quantitative reliability growth modelling, and system dynamics simulation. The analysis is based on empirical data collected from the AMOS computerised maintenance management system for ship propulsion gear over the course of 20,000 operating hours. The Ishikawa diagram is applied as a qualitative tool to structure potential failure causes related to human, technical, material, procedural, measurement, and environmental factors. Using a system dynamics approach, a qualitative conceptual model of cause-and-effect relationships and a quantitative simulation model were developed, where the mathematical model of Goel–Okumoto reliability growth was applied to quantitatively describe the process of detecting and eliminating failures, with an exponential decrease in failure intensity over time and a high level of agreement with empirical data (R2 = 0.9962), corresponding to the part of the bathtub curve related to the running-in of ship systems. The system dynamics simulation implemented in the POWERSIM environment integrates the analytically estimated model parameters and provides a dynamic representation of the relationships between failure intensity, cumulative failures, reliability, and the mean time between failures. The scientific contribution of this work lies in the structured integration of established methods into a single analytical framework, enabling coherent interpretation of empirical reliability data under real operating conditions. The results provide a methodological basis for developing predictive maintenance tools, optimising maintenance strategies, and improving the safety of ship propulsion systems.