Side sensitive group runs $\bar{{X}}$ chart with estimated process parameters

Abstract

The Side Sensitive Group Runs (SSGR) $\bar{{X}}$ chart integrates the $\bar{{X}}$ chart and an extended version of the conforming run length chart. The SSGR $\bar{{X}}$ chart was developed to detect changes in the process mean. The SSGR $\bar{{X}}$ chart was proven to be effective for detecting small and moderate shifts compared with the $\bar{{X}},$ synthetic $\bar{{X}}$ and group runs $\bar{{X}}$ charts, when process parameters are known. However, in reality, process parameters, such as the in-control mean and standard deviation are rarely known. Therefore, these process parameters are estimated from an in-control Phase I dataset. In this article, we investigate the performance of the SSGR $\bar{{X}}$ chart, based on the average run length criterion, when process parameters are estimated. It is shown that differences in the chart’s performance exist, when process parameters are known and when they are estimated, due to the variability in estimating the process parameters. A study is conducted to find the minimum number of Phase I samples required (based on several sample sizes) so that the SSGR $\bar{{X}}$ chart with estimated process parameters behaves approximately the same as its known process parameters counterpart. To facilitate process monitoring and to avoid the need to use large number of samples in the Phase I process, this research develops an optimization procedure using the Scicoslab program to find suitable optimal charting parameters of the SSGR $\bar{{X}}$ chart with estimated process parameters. This program can be requested from the first author.