Combined Shewhart–EWMA control charts with estimated parameters

Abstract

Shewhart and EWMA control charts can be suitably combined to obtain a simple monitoring scheme sensitive to both large and small shifts in the process mean. So far, the performance of the combined Shewhart–EWMA (CSEWMA) has been investigated under the assumption that the process parameters are known. However, parameters are often estimated from reference Phase I samples. Since chart performances may be even largely affected by estimation errors, we study the behaviour of the CSEWMA with estimated parameters in both in- and out-of-control situations. Comparisons with standard Shewhart and EWMA charts are presented. Recommendations are given for Phase I sample size requirements necessary to achieve desired in-control performance.

Keywords:

• control charts
• exponentially weighted moving average
• Shewhart control chart
• average run length
• integral equation
• uncertainty modelling

AMS Subject Classification :

• 62F03
• 62P30
• 62L99

Acknowledgements

The authors thank editors and the anonymous referee for their timely review and many helpful comments that greatly improved the article. This research was partially funded by Italian MIUR-Cofin 2006 grants.