Bilal M. Ayyub
This chapter addresses methods for assessing the probability of failure of individual components. Analytical performance-based approaches are introduced, including performance functions, moment methods, Monte Carlo simulation, and time-dependent reliability analysis. The chapter also presents empirical reliability analysis using life data, covering failure and repair processes, data types, availability, reliability functions, and hazard rates. Methods for selecting and fitting probabilistic reliability models are discussed, supported by illustrative examples and a detailed case study involving hydropower equipment. The chapter emphasizes the integration of analytical and data-driven approaches to quantify component-level uncertainty, providing essential inputs for system-level risk and reliability assessments.