Design of an Exponentially Weighted Moving Average (EWMA) and An Exponentially Weighted Root Mean Square (EWRMS) Control Chart

Abstract

Some of the most widely-used form of control charts Walter Shewhart charts are sensitive to detecting relatively large shifts in the process. On Shewhart charts every observation is plotted independently of previous observations.The quantity plotted on Cusum charts include all previous observations; All of which are given equal weight in calculating the plotted value. Exponentially Weighted Moving Average (EWMA) charts are a kind of compromise between these two extremes. The plotted quantity is a weighted average of all the observations to date, but the weights decrease very quickly backwards in time, so that the most recent observations are the main determinants of the current plotting point.[3][4] A cumulative sums (CUSUM) charts plot the of the deviations of each sample value from a target value. It has been used in various industries (especially the chemical industry) and the form of the CUSUM has been refined over the years to further increase its sensitivity. Two types of charts are primarily used to detect smaller shifts, namely Cumulative Sum (CUSUM) charts and Exponentially Weighted Moving Average (EWMA) charts. E.S.Page2 (1954) originally developed the CUSUM chart. [2][3] Geometric moving–average control chart is effective alternatives to the Shewhart control chart may be used when small process shifts are of interest primarily used to detect smaller shifts, namely CUSUM and EWMA charts are excellent alternatives to the Shewhart control chart. EWMA methodology - developed by S.W. Robert in 1959, he chose the weights to decrease geometrically with the age of the observations, he referred to the control chart based on such a weighting system as a geometric moving –average control chart. Mac Gregor and Harris (1993) recommend that the square root of EWMS, SQR (EWMS), be plotted. Accordingly, they call the corresponding control chart an exponentially weighted root mean square (EWRMS) chart, The EWRMS statistic will react not only to shifts in the process variance but also shifts in the process mean[4] [8]