The Robustness of the Three-Way Chart to Non Normality

Abstract

In batch processing, the Three-Way control chart has been offered for controlling the mean of a process when the batch-to-batch variation is much greater than the within-batch variation. These two sources of variation are typically monitored along with usual batch sample means. Although the Three-Way chart was originally developed for normally distributed process data, its robustness to violations of the normality assumption is the central theme of this study. For data streams with heavy tails or displaying skewness, the in-control average run lengths (ARLs) for the Three-Way chart are seen to be significantly shorter than expected. On the other hand, out-of-control ARLs are much longer than the normal theory benchmarks for symmetric non-normal distributions. The Three-Way chart is not robust to moderate or strong skewness.

Keywords:

• Average run length
• Three-Way control chart
• Variance components

Mathematics Subject Classification:

• 62L20
• 62P30
• 49J22