The generally weighted moving average control chart for monitoring the process mean of autocorrelated observations

The statistical process control chart is primarily applied to monitor the production process or service process and detect the process shifts as soon as possible. The EWMA (exponentially weighted moving average) control chart has been widely used to detect small shifts in the process mean. Sheu and Lin (Qual Eng 16:209-231, 2003) proposed the GWMA (generally weighted moving average) control chart, for detecting small process mean shifts of independent observations. The GWMA control chart is the extended version of EWMA control chart. The GWMA control chart has been widely investigated. In this paper, the definition, and properties of the GWMA control chart are being further analyzed and investigated for detecting small process mean shifts of autocorrelated observations. The weight of GWMA technique depends on time t. Thus, there is no recursive formula for the GWMA technique. The GWMA technique has no Markovian property. The GWMA control chart is more practical for detecting small process mean shifts of autocorrelated observations. A numerical simulation comparison shows that the GWMA control chart outperforms the EWMA control chart for detecting small process mean shifts of autocorrelated observations.