A CUSUM Scheme with Variable Sample Sizes and Sampling Intervals for Monitoring the Process Mean and Variance

摘要

The adaptive control feature and CUSUM chart are two monitoring schemes that are much more effective than the traditional static Shewhart chart in detecting process shifts in mean and variance. However, the designs and analyses of the adaptive CUSUM chart are mathematically intractable and the operation is very laborious. This article proposes a VSSI WLC scheme, which is a weighted-loss-function-based CUSUM (WLC) scheme using variable sample sizes and sampling intervals (VSSI). This scheme detects the two-sided mean shift δ_μ and increasing standard deviation shift δ_σ based on a single statistic WL (the weighted loss function). Most importantly, the VSSI WLC scheme is much easier to operate and design than a VSSI CCC scheme which comprises three individual CUSUM charts (two of them monitoring the increasing and decreasing mean shifts and one monitoring the increasing variance shift). Overall, the VSSI WLC scheme is much more effective than the static X&S charts (by 72.36%), the VSSI X&S charts (by 30.97%) and the static WLC scheme (by 50.94%) for detection. It is even more effective than the complicated VSSI CCC scheme for most cases.