A HYBRID EWMA CONTROL CHART FOR MONITORING PROCESSES FOLLOWING THE WALD (INVERSE GAUSSIAN) DISTRIBUTION: A SIMULATION-BASED APPROACH WITH R IMPLEMENTATION

Abstract

This study proposes a Hybrid Exponentially Weighted Moving Average (HEWMA) control chart specifically designed for monitoring process means when the underlying data follow the WALD (Inverse Gaussian) distribution, a distribution commonly encountered in reliability, lifetime, and first-passage time processes. Traditional Shewhart and standard EWMA control charts rely heavily on normality assumptions and symmetric control limits, which lead to inflated false alarm rates and unstable in-control performance when applied to positively skewed data. To address this limitation, the proposed HEWMA–WALD chart integrates a double-smoothing mechanism with distribution-specific calibration to enhance sensitivity to small and moderate process shifts while maintaining statistical validity. A comprehensive Monte Carlo simulation framework is developed in the R environment to determine control-limit multipliers that stabilize the in-control Average Run Length (ARL₀) at a desired nominal level. The out-of-control performance of the proposed chart is evaluated using key run-length metrics, including ARL₁, standard deviation of run length, and median run length, across varying degrees of skewness and shift magnitudes. Comparative results demonstrate that the HEWMA–WALD chart consistently outperforms the conventional EWMA chart, particularly in detecting small mean shifts, without sacrificing performance for larger shifts. The study further provides a complete and reproducible R implementation along with a practical case study, facilitating real-world adoption. Overall, the proposed methodology offers a robust and efficient monitoring tool for skewed, reliability-oriented processes where early detection of degradation is critical.