A New EWMA Chart Based on Weighted Loss Function for Monitoring the Process Mean and Variance

With the weighted loss function, a new single Exponential Weighted Moving Average (EWMA) chart (WLE chart hereafter for short) is proposed to detect both mean and variance shifts simultaneously. It includes the EWMA control chart based on the semicircle statistic and weighted-loss-function control chart as special cases. Numerical studies show that the WLE chart is superior to the weighted-loss-function Cumulative Sum (CUSUM) chart when the mean and standard deviation shifts are both small, and offers at least comparable detection ability with the WLC chart in other cases. Compared with the Shiryaev-Roberts chart, the WLE chart has a better or comparable performance except for small and moderate mean shifts. Furthermore, an equivalent form of the WLE chart is developed to diagnose the source and direction of a process change.