BAYESIAN CONTROL CHARTS FOR REAL-TIME MONITORING OF DEFECT RATES IN AUTOMATED PRODUCTION LINES USING BINOMIAL AND POISSON MODELS

Abstract

The increasing demand for high-quality automated manufacturing systems necessitates real-time and reliable monitoring solutions to solve production issues. Traditional control charts, such as Shewhart, Exponentially Weighted Moving Average (EWMA), and Cumulative Sum Control Chart (CUSUM), rely on set detection limits and struggle to handle tiny shifts across different sample sizes. This study creates and assesses Bayesian control charts based on the Binomial and Poisson models for real-time defect rate monitoring in automated production lines. The Bayesian Binomial chart monitors defect proportions in batch processes, while the Bayesian Poisson chart tracks defect numbers over time. The suggested approach reduces the in-control average run length (ARL₀) by 47% compared to Shewhart and 25% compared to EWMA, based on simulation of 2,000 replications with a sample size of 200. Small shifts (0.25σ - 0.50σ) resulting in a 45% reduction in out-of-control ARL₁, showing increased sensitivity. The model has lower Type I (0.038) and Type II (0.055) error rates, a p-value of 2.2×10⁻¹⁶, and a Bayes factor (Bf₁₀) of 18.6. These studies show that Bayesian Binomial and Poisson charts improve fault detection, reduce false alarms, and increase decision-making efficiency in automated manufacturing systems.