Effect of the Smoothing Parameter on Nonparametric Improved Recursive Double Homogeneously Weighted Moving Average Control Chart

Abstract

The study investigates the effect of varying the power of the smoothing parameter (λ) in a Nonparametric Improved Recursive Double Homogeneously Weighted Moving Average control chart based on the Wilcoxon Signed-Rank statistic (NPIRDHWMA-WSR) for enhanced process monitoring. Specifically, the research examines the influence of smoothing parameter powers ranging from λ⁴ to λ⁸ on the detection capability of the chart. A Monte Carlo simulation with 5,000 iterations was conducted under different process distributions, including normal, contaminated normal, and heavy-tailed distributions, to evaluate the Average Run Length (ARL) performance of the proposed configurations. The results show that increasing the smoothing parameter power improves detection sensitivity for moderate process shifts, with the λ⁶ configuration providing the best balance between rapid detection and stability while maintaining the desired in-control performance (ARL₀ ≈ 500). Furthermore, the proposed chart demonstrates strong distributional robustness across all tested scenarios. The practical applicability of the method was validated using wine quality data, where the chart successfully detected process shifts in chloride measurements, identifying out-of-control signals beginning around samples 18–19 and producing 22–23 alarms within 40 observations. Overall, the NPIRDHWMA-WSR control chart provides a flexible and effective tool for monitoring industrial processes under non-normal conditions, offering practitioners an evidence-based approach for selecting smoothing parameter configurations that balance detection speed and false alarm stability.