This study develops an approximate analytical model for assessing production risks in manufacturing systems with sequential technological operations under uncertainty. While stochastic models allow detailed representation of production processes, their practical application is often limited by high computational complexity. To address this issue, an analytical approximation framework is proposed, enabling efficient evaluation of processing time under the influence of production risks. The model is based on a probabilistic interpretation of risk using a normalized risk priority index (WJRPN), which allows integrating the impact of 4M factors (Man, Machine, Material, Method) into the stochastic description of operation durations. Analytical expressions are derived for the expected value and variance of inter-operational delays, forming the basis for the pro-posed approximate model of batch processing time. A key advantage of this approach is a significant reduction in computational complexity compared to trajectory-based sto-chastic models while maintaining acceptable accuracy. Numerical results show that the relative error of the model does not exceed 5%, making it suitable for engineering ap-plications. The developed model provides a practical tool for rapid analysis of production lines, enabling risk-aware planning, identification of critical operations, and improve-ment of manufacturing system reliability.