Phase II monitoring of variability using Cusum and EWMA charts with individual observations

Abstract

When monitoring a process mean in Phase II, it is well known that time-weighted control charts (such as the Cusum or EWMA) of individual observations are more sensitive for detecting small mean changes than are the traditional Shewhart control charts for individuals. Further, by collecting one observation every 12 minutes, rather than a subgroup of five every hour, the time-weighted charts of individual values result in a shorter ATS (average time to signal) than would be possible using Shewhart charts of subgrouped data. This article explores a similar strategy of monitoring process variability using time-weighted control charts and individual observations. The average time to signal a change in variability using these charts is studied when there are targets or known values for the in-control process mean and standard deviation. The results show that the ATS of both the Cusum and EWMA are substantially shorter than the ATS for the standard R charts or the more efficient S2 chart using subgroups of 5. The article also describes how the control limits for the EWMA chart to monitor process variability should be modified if the in-control process mean and standard deviations are unknown and must be estimated from a Phase I study. Computer functions that are available in R packages for creating Cusum-EWMA charts and computing their ARL (average run length) are demonstrated in this study and are included in the appendix.