Adaptive CUSUM of the Q chart

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.