Production line balancing is a fundamental challenge in manufacturing operations, directly influencing throughput, resource utilization, and operational cost efficiency. Despite decades of research, many industrial production lines continue to operate with significant imbalances: idle time accumulates at certain workstations while bottlenecks persist at others, primarily because existing balancing approaches treat task times as deterministic and fail to account for the inherent statistical variability present in real manufacturing environments. This study develops a comprehensive statistical framework for production line balancing that explicitly incorporates task time variability, regression-based idle time modeling, and probability-adjusted cycle time estimation. Using 45 time study observations collected across five workstations of a simulated manufacturing line, the framework applies descriptive statistics, multiple regression analysis, one-way ANOVA, and stochastic cycle time modeling to identify and quantify the principal sources of line imbalance. Results demonstrate that the proposed optimized balancing configuration achieves a line efficiency of 94.3%, compared to 68.4% under the current unbalanced arrangement   a gain of approximately 26 percentage points. Regression analysis identifies task time variance, precedence complexity, and setup change frequency as the three most statistically significant predictors of idle time, together explaining 86.1% of its variation. The ANOVA confirms that differences in line efficiency across four balancing methods are statistically significant (F = 47.62, p < 0.001). The findings provide production engineers and operations managers with a statistically grounded, practically implementable methodology for systematic line balancing improvement.

Keywords: production line balancing, statistical process control, regression analysis, cycle time optimization, ANOVA, operations research.