A study on the effects of trends due to inertia on EWMA and CUSUM charts

Abstract

Unlike a Shewhart chart, the exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts are memory control charts (also known as time weighted control charts) that are used for a quick detection of small shifts in the process mean. Control charts that combine information from present and past samples, like the EWMA and CUSUM charts have the ability to detect process changes based on past information. A trend could exist on the EWMA and CUSUM charts, where all the sample points fall in one particular direction on the charts, for example, only above or below the center line. For this case, if a shift in the process mean occurs in the opposite sides of the chart, then such a shift cannot be detected quickly. This phenomenon is known as the inertia problem. A simulation study is conducted using Statistical Analysis System (SAS) to study and compare the effects of inertia on EWMA and CUSUM charts. It is found that the EWMA chart is affected by the inertia problem but not the CUSUM chart