Design of Multiple Cause-Selecting Charts for Multistage Processes with Model Uncertainty

Abstract

The cause-selecting chart (CSC) is an effective statistical process control tool for monitoring multistage processes. The multiple cause-selecting chart (MCSC) is the further development of the CSC, which deals with the case when the output measure is a function of multiple input measures. In practice, the model relating the input and output measures often needs to be estimated before the MCSC is implemented. However, the traditional design of MCSCs does not take parameter uncertainties into account when estimating the control limits. The actual false-alarm rate can substantially differ from what is expected. This article presents the design and implementation of MCSCs using prediction limits to account for parameter uncertainties. These limits are developed using two types of procedures: the least-squares estimation and principal component regression. The simulation results show that the prediction limits are quite effective in terms of maintaining a desired false-alarm rate.

Keywords:

• Statistical process control
• Principal components regression

Acknowledgment

The authors are grateful to the editor and the referee for their valuable comments. F. Tsung's research was supported by RGC Competitive Earmarked Research Grants HKUST6073/00E, HKUST6011/01E and HKUST6183/03E.