Bootstrapped-based cumulative sum and exponentially weighted moving average control charts: Enhanced process control

This study addresses challenges in Phase II univariate process control, where in-control data exists but underlying process distributions are unknown. Traditional control charts often require specific knowledge of these distributions, which is impractical in many real-world applications. This paper proposes novel control charts, the Bootstrap-Based Cumulative Sum-Exponentially Weighted Moving Average (BCUSUM-EWMA) charts, designed for any process (mean or variability) monitoring. These charts utilize bootstrapping to overcome limitations imposed by normality assumptions, which may not hold true in practice. The new BCUSUM-EWMA chart was compared with bootstrap-based CUSUM (BCUSUM) and EWMA (BEWMA) charts. The performance of these charts was evaluated using Average Run Lengths (ARLs) and Standard Deviation run Lengths (SDRLs) calculated via Monte Carlo simulation in R software. To demonstrate the practical application of our proposed BCUSUM-EWMA control chart, we analyzed real-world wearer heart rate data from 37 patients collected from the record office at Irrua Specialist Teaching Hospital. We employed a bootstrap simulation of 1500 samples to evaluate the chart's performance. Compared to classical control charts, the bootstrap-based charts signal out-of-control shifts earlier. Additionally, performance assessment based on ARLs and SDRLs confirms the effectiveness of the bootstrap approach, with smaller out-of-control Run Lengths indicating earlier detection.