Fatigue cracks in welded components can cause loss of structural integrity and failures of structural systems. To ensure the safety and reliability of deteriorating structural systems, system damage should be detected as early as possible through inspection, and timely maintenance or repair is required. Delays in damage detection lead to maintenance or repair delays, which adversely affect structural integrity and functionality. In this study, a probabilistic approach to quantify the reliability of deteriorating structural systems with explicit damage detection delay computations was developed for the first time and applied to an offshore structural system. To obtain the system damage detection delay, the system damage occurrence and detection times were rationally defined. Subsequently, the effects of different inspection strategies on system damage detection delay were studied. Finally, the relationship between system reliability and system damage detection delay was investigated. The results show that the system damage detection delay decreases as the inspection quality, number of inspections, or number of components inspected simultaneously increases. It is interesting to determine the law of diminishing marginal system damage detection delay. In addition, there is an approximately negative linear relationship between the system reliability index and system damage detection delay.