CUSUM AND EWMA CHARTS FOR MONITORING A PROCESS VARIANCE

Abstract

Part I: Optimal Designs of CUSUM Control Charts for Monitoring a Process Variance

Cumulative sum ( CUSUM) Control charts have been widely used for detecting shifts in the process rnean. Relatively little attention has been given to the use of CUSUM charts for monitoring the process variance. CUSUM charts based on the log transformation of sample variance (S2) for detecting changes in the process variance are proposed here. Optimal design for the one-sided and two-sided CUSUM charts arc developed.

The fast initial response enhancement to the CUSUM charts are also discussed. The effects of nonnormality and serially correlated observations on the perfermance of the CUSUM chart are also studied thoroughly. A comparison in terms of averagc run lengths (ARLs) between CUSUM charts based on S2 and log(S2 ) is also considered. An extensive comparison of the performance of CUSUM and EWMA charts based based on log(S2) for monitoring the process variance is presented. It is found that the performance of a CUSUM chart is comparable to that of the corresponding EWMA chart.

Part II: Optimal Designs of One-Sided and Two-Sided EWMA Charts for Monitoring a Process Variance

The purpose of including a reflecting boundary in a one-sided exponentially weighted moving average ( EWMA) control chart is to prevent the EWMA from drifting too far away from the target value in response to a few large sample values. In such a case an EWMA chart would be slow to react to a sudden out-of-control situation. The effect of the reflecting boundaries of one-sided EWMA charts are investigated and reasonable choices of reflecting boundaries are determined. The EWMA chart has been proposed for detecting increases in the process variance; however, detecting increases in the process variance is at least as important as detecting increases. Optimal design procedures are developed for designing one-sided and two-sided EWMA charts.

Plots of the optimal chart parameters are provided and can be used easily to design an optimal EWMA chart. The EWMA charts recommended here are found to be more sensitive than the cumulative sum charts in detecting small and moderately large changes in the process variance and only slightly less sensitive for large changes.