EWMA Chart Based On Weighted-Loss-Function

In statistical process control(SPC), when dealing with a quality characteristic that is a variable, it is usually necessary to monitoring both the mean value of the quality characteristic and its variablity. The X-S or X|--R, CUSUM_X|-&CUSUM_S, EWMA_X|-xkEWMA_S control charts have been used widely for this purpose in manufacturing industry. These control charts are combined scheme.But the combined scheme is sometimes inconvenient and time-consuming. For example, the problem about the computation of the Average Run Length(ARL). So in the recent ten years, some charting schemes that use a single chart to monitoring both mean and variance have been proposed. These include the L chart (the Loss Fuction control chart)(Chao and Cheng(1996)), the WL chart(the Weighted Loss Function chart)(Wu and Tian(2002)), the LE chart(the EWMA chart which based on the Loss Fuction)(Chen etc(2004)), the WLC chart(the CUSUM chart which based on the Weighted Loss Function) (Wu and Tian(2002)).Based on the Weighted Loss Function, our article proposes a EWMA chart (called WLE chart) that detects both mean shifts and variance shifts, and discusses the method of the ARL computation, morveover, We give a comparatively optimal WLE chart.The one advantage of the WLE chart is its simplicity for implementation and design compared with the X|--S or X-R chart, CUSUM_X|-&CUSUMs chart, EWMA_X|-&EWMA_S chart.The another advantage of the WLE chart is its effienciency when the process mean and variance shifts is small or morderate compared with the LE chart.The WLE chart performances better than the WLC chart when the process mean a-nd variance shifts is small. In other cases, the detection results of the WLE chart and the WLC chart have narrow difference, but the implementation and computation of the WLE chart is comparatively simpler.In the end, we proposed a method which is easy to quickly identify the source and the direction of an out-of control point in these charts by decomposing the statistic.