An EWMA Chart With Variable Sample Sizes Based On Weighted-Loss-Function

In statistical process control(SPC), when dealing with a quality characteristic that is a variable, wu usually monitor both the mean value of the quality characteristic and its variablity simultaneously. Such as the X|- - S or X|- - R, CUSUM_X|-&CUSUM_s, EWMA_x|-&EWMA_s control charts, and so on. Now, some charting schemes that use a single chart to monitoring ·both mean and variance have been proposed. These include the WL chart (the Weighted Loss Function control chart)(Wu and Tian(2002)), the WLC chart(the CUSUM chart which based on the Weighted Loss Function) (Wu and Tian(2005)), the WLE chart (the EWMA chart which based on the Weighted Loss Function)(Liang Wenjuan(2006)). These control are more effictive than those charts. These kind of control charts are named as static charts(i.e. using fixed sample size, sampling interval and control limits), its has the advantage of easy design and operation. However, its effectiveness in detecting process shifts is generally less adequate than that of the charts with adaptive charts.A VSS chart becomes favoured under certain circumstances where the sample size can be easily varied but the sampling intervals is required to be fixed due to some managerial and/or operational reasons. Many research works have been published on the VSS schemes.From the EWMA chart based on weighted-loss-function and variable sample sizes CUSUMchart based on weighted-loss-function, we proposes an EWMA chart based on the weighted-loss-function with variable sample sizes (called VSS WLE chart) that detects both mean shifts and variance shifts, proposes a new method, called collocated integral, and put it into the new chart, we discusse the optimality of the VSS WLE chart, compared it with other charts, in the end, we distinguish the type of the shifts by decomposing statistics.