The construction industry, known for its dynamic and chaotic nature, often experiences work accidents. Existing planning methods addressing uncertainties, however, frequently overlook safety variables, and the relevant literature is scarce. This study introduces a novel construction planning method focused on investigating the impact of safety incidents on project duration, specifically in energy infrastructure construction projects. The main hypothesis is that safety events during construction significantly affect project duration, leading to deficient schedules when not considered in the planning process. Utilizing stochastic process theory, particularly the quasi birth and death process, the study explores how safety states influence delay states. Neural network models complement the stochastic model for forecasting bivariate time series derived from safety and delay stochastic states. Real-life project data demonstrates that safety events, assuming planned delay events, are over double the delay states value. Applying the stochastic model to a real project with a planned 8-day delay indicates a most probable safety state of 19. Long short-term memory models outperform statistical methods in bivariate time series forecasting, with a significantly smaller root mean square estimation metric. The proposed hybrid construction planning approach proves suitable for both pre-construction and construction phases, offering improved decision-making indicators and supporting reactive safety management.