For decades control charts have been used as effective tools for detecting process changes that may affect the quality of products and services. Usually, the parameters of the process are unknown and are estimated from the Phase I process data before being used to construct control charts for Phase II process monitoring. Using parameter estimates to construct Phase II charts is known to degrade chart performance, for example the in-control average run-length of the chart may be shorter than nominally expected, causing higher false alarms. These effects of parameter estimation on control chart properties have been widely studied. However, the question of “how to adjust the Phase II limits to compensate for the effects of parameter estimation?” still needs further investigation.
My research focuses on the latter issue, specifically on numerically finding the correct charting constants of a Phase II chart with estimated limits, based on a given amount of Phase I data and a given nominal value of some control chart performance criterion. It also compares this numerical approach with other approaches such as the bootstrap.