Directed control charts for detecting the shape changes from linear profiles to quadratic profiles

Abstract

In profile monitoring, control charts are constructed to detect any unanticipated departures from the statistical stability of product quality over time, where product quality is characterised by a function. In many situations, due to the characteristics of a system or an operation, certain process signals can be anticipated. Thus, when a kind of departure specifically feared is identified in advance, a directed process monitoring approach can be developed. Motivated by the monitoring of cylindrical surfaces, this paper focuses on quickly detecting the shape changes from a straight line to a second-order polynomial curve. Based on the hypothesis testing on the quadratic term, two directed control charts and a combined scheme are proposed to surveillance the sampled linear shape. The performance of our proposed methods is studied and compared with the alternative charts by numerical simulations. Simulation studies show that the two proposed directed charts are almost the same, and outperform the alternative methods in some cases. Moreover, the combined scheme is robust for all the parameter combinations.

Keywords:

• average run length (ARL)
• directed process monitoring
• profile monitoring
• second-order regression
• statistical process control (SPC)

Acknowledgements

The authors thank the editor and two anonymous referees for their valuable comments that lead to the significant improvements in the article. The authors would also like to thank Brahim Laalej at National Engineering School of Val de Loire (ENIVL), France, for his helpful comments on the paper.

Funding

This research was supported by National Natural Science Foundation of China [grant number 70931004], [grant number 71225006], [grant number 70802043] and [grant number 71102140].