Time-dependent Bayesian dynamic probabilistic duration forecasting of underground construction activities

Purpose Underground construction activities are subject to substantial geological and operational uncertainty, making reliable duration forecasting difficult during project execution. This study proposes a time-dependent Bayesian duration forecasting (TDBDF) method to provide accurate dynamic probabilistic forecasts. Design/methodology/approach The TDBDF method integrates on-site observation data into a probabilistic model to update the final duration estimation. Specifically, the Beta cumulative distribution function is adopted to model the cumulative progress curve, while Bayesian inference with Markov chain Monte Carlo is applied to update the duration forecasts as new progress data becomes available. A time-dependent weighted likelihood function is further introduced to assign greater influence to more recent observations in posterior updating. Findings Case-based validation using two underground construction activities from a real-life project shows that TDBDF method enables continuous probabilistic updating of final duration forecasts and provides credible intervals for schedule risk. Compared with the conventional earned schedule method, it achieves better forecasting performance, particularly in the early stages. The proposed time-dependent weighting strategy reduces the mean absolute percentage error (MAPE) by 2.36% relative to the unweighted probabilistic model. Sensitivity analysis further reveals that the initial estimation of duration has the greatest impact on forecasting performance. Originality/value This study extends Bayesian duration forecasting from static prior-data fusion to dynamic updating for ongoing underground construction activities, and introduces a time-dependent weighted likelihood to capture the unequal importance of sequential progress observations. The proposed TDBDF framework is particularly suitable for small-sample, high-uncertainty construction environments, where continuous updating and risk assessment are critical for schedule control.