Statistical Design for Monitoring Process Mean of a Modified EWMA Control Chart based on Autocorrelated Data

Abstract

From the principles of statistical process control, the observations are assumed to be identically and independently normally distributed, although this assumption is frequently untrue in practice. Therefore, control charts have been developed for monitoring and detecting data which are autocorrelated. Recently, a modified exponentially weighted moving average (EWMA) control chart has been introduced that is a correction of the EWMA statistic and is very effective for detecting small and abrupt changes in independent normally distributed or autocorrelated observations. In this study, the performance of a modified EWMA chart is investigated by examining the 2 sides of the exact average run length based on an explicit formula when the observations are from a general-order moving average process with exponential white noise. A performance comparison of the EWMA and the modified EWMA control charts is also presented. In addition, the performance of the modified and EWMA control charts is contrasted using Dow Jones composite average from a real-life dataset. The findings suggest that the modified EWMA control chart is more sensitive than the EWMA control chart for almost every case of the studied smoothing parameter and constant values of the control chart.
 HIGHLIGHTS
 
 Autocorrelation data is frequency untrue of assumption practice in time series data
 Modified EWMA is a new control chart that is effective for detecting change in independent normal distribution and autocorrelated observations
 The efficiency of the control chart is measured by average run length
 Explicit formula is easy to derive and provides the exact value of the average run length