EWMA Control Chart for Monitoring Circular Data

ABSTRACT In quality control applications, it is crucial to determine whether the data remains in statistical control or has deviated into an out‐of‐control state. The exponentially weighted moving average (EWMA) control chart is particularly effective for identifying changes in distribution, especially when shifts from in‐control to out‐of‐control conditions are moderate or small, while Shewhart charts are effective in detecting large shifts. This paper presents EWMA and Shewhart control charts specifically designed to detect changes in both the location and concentration of circular data that follows the well‐known circular von Mises distribution. The performance of the proposed charts is evaluated by using Monte Carlo simulation, and their efficacy is validated through application to real data. Results reveal that both charts showed directional invariance property in monitoring location for von Mises data with different true mean direction values. The EWMA chart shows superiority in identifying small to moderate shifts, while the Shewhart chart exhibits slightly better results for detecting large shift values. As for monitoring concentration, the EWMA chart generally gives better results.