Continuous-Time Markov Chain Modelling for Service Life Prediction of Building Elements

A continuous-time Markov chain framework is developed for service life prediction of building assets, and three formulations are compared: a homogeneous generator, a time-varying generator, and a fractional model. The framework delivers survival, density of absorption time, hazard, and mean time to absorption. For the homogeneous case, state trajectories are computed using matrix exponentials. The time-varying case is solved both by local exponential propagation on a time grid and by direct integration of the Kolmogorov equation. The fractional case is implemented in two independent ways, via a truncated series expansion and via an in-house routine for the Mittag-Leffler function, which also allows the direct evaluation of survival and hazard from the standard fractional relations while avoiding singular behaviour at the origin. This study shows that non-homogeneous rates accelerate deterioration relative to the homogeneous benchmark, whereas fractional dynamics reproduce early-time acceleration followed by a slow decline of the hazard, which is consistent with heavy-tailed survival and longer effective service life. The two fractional solvers provide mutually consistent outputs, which supports the numerical robustness of the approach. The framework is readily applicable to sparse inspection data and short observation windows and provides a transparent basis for comparing modelling assumptions that affect life cycle forecasts used in asset management and maintenance planning.