A New Nonparametric Generally Weighted Moving Average Chart With Moving Sign

ABSTRACT

Control charting techniques have been widely used in industries to monitor a process for quality improvement. A nonparametric (NP) or distribution‐free technique is used in practice to evaluate the characteristics of data that do not follow a normal distribution or are often unknown. A novel NP control chart based on the Generally Weighted Moving Average (GWMA) utilizing the moving sign (MS) test statistic is proposed to improve monitoring of process location. The GWMA chart serves as the exponentially weighted moving average (EWMA) chart when the adjustment parameter equals one. Monte Carlo simulations evaluate performance across statistical metric properties, including average run length (ARL), standard deviation of run length (SDRL), extra quadratic loss (EQL), average extra quadratic loss (AEQL), relative ARL (RARL), and performance comparison index (PCI), with results benchmarked against NP‐EWMA‐S, NP‐GWMA‐S, and NP‐EWMA‐MS charts. In the evaluated scenarios, NP‐GWMA‐MS chart achieves the smallest EQL and AEQL, and the lowest relative mean index (RMI). The performance of the proposed NP‐GWMA‐MS chart is not optimal in all scenarios but can compete with existing compared NP charts. An illustrative application is presented to demonstrate the practical utility of the new chart. The findings suggest that the proposed chart offers a reliable tool for quality and industrial engineers in process monitoring tasks.