Effects of estimation errors on cause-selecting charts

The Cause-Selecting Chart (CSC) is a useful statistical process control tool for analyzing multistage processes. It distinguishes between incoming and outgoing quality problems by establishing a relationship between input and output measurements. In practice, the model relating the input and output must first be estimated before the CSC is implemented. Most previous work on CSCs has focused on the case when the model is estimated without error. Far less is known about the performance of CSCs with parameter estimation errors. This paper investigates the effect of parameter estimation errors on the performance of CSCs. The results indicate that the charted statistics are correlated after parameter estimation. It is also shown that this correlation will increase as the mean shift in the input increases. The implications for the use of CSCs when parameters are estimated are discussed, including the use of widened control limits and self-starting procedures.

Acknowledgements

The authors are grateful to the editor, department editor, and anonymous referees for their valuable comments. F. Tsung's work was supported by RGC Competitive Earmarked Research Grants HKUST6011/01E and HKUST6183/03. L. J. Shu was supported in part by the Research Committee in University of Macau under grant RG018/02-03S.