A computationally efficient self-starting scheme to monitor general linear profiles with abrupt changes

Abstract

A self-starting monitoring scheme is proposed in this paper for the simultaneous detection of variance and coefficients in linear profiles with unknown error distributions. Based on the global data, we construct a sequential Wald-type charting statistic, obtain the corresponding asymptotical distributions and further provide a recursive algorithm to quickly calculate statistics sequentially. Control limits of our charting statistics are also constructed based on their asymptotical distributions. Finally, we apply our method to analyze both artificial and real data, and numerical results show that our method performs well.

Keywords:

• Linear profile
• self-starting
• SPC
• Wald-type charting statistic

Acknowledgements

The authors are grateful for constructive comments from the editor and all referees.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Prof. Tsung was supported by RGC GRF [grant number 16203917]; Prof. Xia was supported by National Natural Science Funds of China [grant number 11771353], [grant number 11201372]; Research Grants Council, University Grants Committee [grant number 619913].