Calendar‐Time and Gap‐Time Reliability Assessment of Repairable Tide‐Gauge Systems Using Crow–AMSAA and Hierarchical Weibull Models

Abstract

Coastal tide‐gauge stations are critical components of ocean observing networks, yet their operational reliability is rarely assessed using formal repairable‐system methods. This study presents a dual‐time‐scale reliability assessment of all‐cause functional service interruptions at two long‐operating Portuguese tide‐gauge stations. Calendar‐time failure trends were evaluated using Crow–AMSAA non‐homogeneous Poisson process models, whereas operating spells between restorations and subsequent failures were analysed using a common‐shape Weibull model with station‐specific scale parameters and Bayesian uncertainty quantification. The Crow–AMSAA analysis provided no statistically significant evidence of reliability growth or deterioration at either station (Leixões: , 95% CI 0.521–1.483; Sines: , 95% CI 0.852–1.364). The posterior median common Weibull shape parameter was 0.568 (95% credible interval: 0.470–0.680), indicating a decreasing gap‐time hazard. The posterior median one‐year RMST was 3495 h at Leixões and 2443 h at Sines. Restoration times were right‐skewed, with median durations of 21.5 and 24.0 h, respectively, while empirical availability was approximately 0.969 at both stations. No finite interior optimum for age‐based preventive maintenance was identified within the evaluated range, and this conclusion remained unchanged across corrective‐to‐preventive cost ratios from 2 to 5. Model checking showed good agreement between the Weibull model and the empirical data at Leixões but identified local lack of fit for the shortest operating intervals at Sines. These findings demonstrate the complementary roles of calendar‐time and gap‐time reliability analyses while highlighting both the strengths and the limitations of parsimonious reliability models based on historical system‐level operational records.