Continuous-Time Hidden Markov Modeling for Remaining Service Life Estimation of Building Elements Under Inspection Uncertainty

Service life estimates derived from inspections depend on both deterioration dynamics and the accuracy of condition assessments. This study develops a continuous-time hidden Markov framework for estimating the remaining service life of building elements from sparse inspection histories. A sequential deterioration model describes progression towards a poor condition threshold requiring major intervention, rather than structural collapse. The framework is implemented in MATLAB 2026a and applied to records of 25 elements from two inspection campaigns. Transition intensities and initial state probabilities are estimated by maximum likelihood for fixed scenarios of inspection error. Posterior condition probabilities are then used to calculate remaining life distributions and survival measures. Sampling variability is assessed by complete weighted enumeration of a stratified bootstrap, while optimization from multiple starting points checks numerical reproducibility. Inspection histories produce different life estimates for elements with identical latest ratings, although the hidden model does not improve data fit over the observable continuous time benchmark. Broad uncertainty in estimated life measures persists despite reproducible optimization, indicating that limited inspection information remains a major constraint within the adopted model. The framework provides a transparent link between uncertain inspections and service life forecasts while distinguishing predictive variability from sampling uncertainty. The findings highlight the need for longer inspection histories, independent calibration of classification errors and validation against subsequent observations.