Explicit analytical solutions for the average run length of modified EWMA control chart for ARX(p,r) processes

Abstract

Statistical process control (SPC) plays a necessary role in manufacturing industry processes. An essential tool for SPC used for monitoring, measuring, controlling, and improving quality in various fields is the control chart. The modified exponentially weighted moving average (modified EWMA) control chart is widely used in various fields, and a measure commonly used to elucidate its efficiency is average run length (ARL). The main purpose of this study is to derive explicit formulas for the ARL to detect changes in the process mean of modified EWMA control chart for an autoregressive processes with explanatory variables (ARX(p,r)) with exponential white noise. In addition, the performances of the modified EWMA are compared with EWMA control charts based on the relative mean index (RMI). It was found that the explicit formulas for the ARL of the modified EWMA control chart performed better than on the EWMA control chart for monitoring process mean.

Keywords

• average run length
• modified ewma control chart
• arx process
• explanatory variables
• integral equation