Standard Deviation of the Run Length (SDRL) and Average Run Length (ARL) Performances of EWMA and Synthetic Charts

Abstract

Statistical process control (SPC) techniques are applied to monitor a process. The control chart is a valuable tool in SPC. the shewhart control chart was the first chart proposed in the literature of SPC and it is still used in process monitoring in today's manufacturing and service industries. both the exponentially weighted moving average (EWMA) and synthetic charts outperform the shewhart control chart for detecting shifts in the process mean. Since both the EWMA and synthetic charts provide better process mean shifts detection performance, a study on which chart to use in process monitoring under different situations is the aim of this work. this paper compares the average run length (ARL) and standard deviation of the run length (SDRL) profiles of the EWMA and synthetic charts. comparisons are made based on the normality assumption. The mathematica programs are used to compute the ARLs and SDRLs of the EWMA and synthetic charts. the ARL results indicate that the EWMA chart is superior to the synthetic chart for detecting small mean shifts, but the latter prevails for detecting moderate and large shifts. however, in terms of the SDRL, the EWMA chart surpasses the synthetic chart for small and moderate shifts. Index Terms—Average run length (ARL), exponentially weighted moving average (EWMA) chart, synthetic chart, standard deviation of the run length (SDRL).