Adaptive CUSUM of the Q chart

Abstract

The CUSUM of the Q chart, as a self-starting approach, was previously proposed for detecting process shifts when the in-control process parameters are unknown. Motivated by the recent development of the adaptive chart, this paper proposes a new self-starting approach that integrates the CUSUM of the Q chart with the feature of adaptively varying the reference value, to better detect a range of shifts with unknown process parameters. The choice of the chart parameters and the masking effect are also studied. Simulation results show that our proposed chart offers balanced protection against shifts of different magnitude, and has performance comparable to the dynamic change-point control scheme. A real example from industrial manufacturing is used to demonstrate its implementation.

Keywords:

• SPC
• quality control
• reliability engineering

Acknowledgements

The authors are grateful to the Editor and the anonymous referees for their valuable comments that vastly improved the paper. This work is supported by the Natural Sciences Foundation of China (10771107 and 10711120448) and Tianjin (07JCYBJC04300).