This paper provides a methodology for the structural reliability analysis of marine vessels based on failure modes of their hull girders, stiffened panels including buckling, fatigue, and fracture and corresponding life predictions at the component and system levels. Factors affecting structural integrity such as operational environment and structural response entail uncertainties requiring the use of probabilistic methods to estimate reliabilities associated with various alternatives being considered for design, maintenance, and repair. Variability of corrosion experienced on marine vessels is a specific example of factors affecting structural integrity requiring probabilistic methods. The Structural Life Assessment of Ship Hulls (SLASH) methodology developed in this paper produces time-dependent reliability functions for hull girders, stiffened panels, fatigue details, and fracture at the component and system levels. The methodology was implemented as a web-enabled, cloud-computing-based tool with a database for managing vessels analyzed with associated stations, components, details, and results, and users. Innovative numerical and simulation methods were developed for reliability predictions with the use of conditional expectation. Examples are provided to illustrate the computations.