Generally weighted moving average control chart in the presence of measurement error via auxiliary information utilization

Abstract

Control charts are essential tools for monitoring the stability of manufacturing processes. However, measurement error can reduce their effectiveness by weakening their ability to detect process shifts. This study introduces an improved version of the Generally Weighted Moving Average (GWMA) chart, called the Auxiliary Information Based GWMA with Measurement Error (AIB-GWMA-ME) chart. This new chart combines auxiliary information with a measurement error adjustment mechanism to improve monitoring accuracy. Three types of measurement error models are considered – namely, the covariate model, multiple measurements model, and linearly increasing variance model. For each model, the statistic of the AIB-GWMA-ME chart is developed, and the corresponding control limits are determined. Monte Carlo simulations are used to assess the chart’s performance based on Average Run Length (ARL). Results show that the AIB-GWMA-ME chart improves sensitivity to small shifts and performs better than existing GWMA and EWMA charts in the presence of measurement error.