Abstract Dynamic reliability analysis must consider both dynamic performance and parametric randomness to evaluate system safety in operation. The saddle-point approximation method is utilized to establish the dynamic probability distribution for known or unknown types of random variables. The cumulative distribution function is used to establish the approximation dynamic reliability model based on a simplified formula with high accuracy. Dynamic reliability analysis is investigated to describe the system safety of the moving operation process. Additionally, dynamic reliability-based sensitivity is used to represent the influence of the parameters on the system's dynamic performance. The fixed-threshold model and load-strength interference model are considered to develop computational formulas of reliability analysis and the degree of effect of each parameter's fluctuation. Finally, the proposed method is evaluated and demonstrated by means of four numerical examples to analyse the system performance and the parameters’ effects. The crude Monte Carlo simulation is performed to provide benchmark results.