Stochastic Modeling of Operation Time Under Production Risks Depending on the Size of the Processed Batch of Parts

This article addresses the problem of production risk assessment in linear manufacturing systems, considering the stochastic nature of equipment downtime and variability in processing times. An original stochastic model is proposed, based on a dimensionless state-space representation of the technological route, which enables a unified analysis of linear production lines under uncertainty. The model incorporates probabilistic characteristics of downtime, raw material defects, and other operational disturbances to evaluate their combined impact on production performance. A risk function is introduced to quantify the probability of exceeding the standard batch completion time. Numerical experiments demonstrate how batch size influences the distribution of processing time and overall production stability. The key contribution lies in integrating the structural characteristics of production systems with probabilistic operational states into a single analytical framework, enabling more accurate estimation of order completion times and improved production planning under uncertainty.