The reliability estimation of machinery systems is a critical aspect of their design and operation, ensuring optimal per-formance and minimal downtime. Traditional methods of reliability analysis often assume precise numerical values for failure rates and operational conditions, which may not always reflect the uncertainty or imprecision inherent in real-world systems. This paper proposes a fuzzy set theory-based approach for estimating the reliability of machinery systems, in-corporating the inherent vagueness and imprecision associated with system parameters such as failure rates, maintenance schedules, and environmental conditions. By representing these parameters as fuzzy sets, the methodology allows for a more flexible and realistic modeling of reliability, accounting for uncertainties that cannot be precisely quantified. The paper discusses the application of fuzzy logic in evaluating the system's reliability index, employing fuzzy arithmetic and fuzzy inference systems. The proposed approach provides a robust framework for assessing the reliability of complex machinery systems, facilitating better decision-making in design, maintenance, and operation. Numerical examples are included to demonstrate the practical application of the method, showcasing its ability to improve the accuracy and rele-vance of reliability predictions in real-world scenarios.

Fuzzy Reliability, Repair Rate, Failure Rate, Switching Failure