Fast Initial Response‐Based Exponentially Weighted Moving Average Maximum Chart for Joint Monitoring the Mean and Variance With Time‐Varying Control Limits

ABSTRACT Joint monitoring of the mean and variance by a single control chart is essential and easy to use in practice. The MAX‐type control schemes provide the solution for detecting the shifts in process mean and variance simultaneously. However, the detection capability of the MAX‐type scheme is often not sensitive during the initial setup of the process. In this paper, a fast initial response (FIR) based MAX‐type scheme is proposed to improve the sensitivity of control charts especially in the initial phase. The proposed scheme extends the exponentially weighted moving average maximum (MAX‐EWMA) control chart to an FIR‐EWMA‐MAX control chart to joint monitor the process mean and variance with time‐varying control limit. We evaluate the average run length and standard deviation of run length performance and compare the proposed control scheme with the existing MAX‐EWMA and the new general weighted moving average maximum (GWMA‐MAX) control charts. Simulation results suggest that the proposed control scheme is more responsive in the initial phase as expected, and performs even better in identifying small shifts in process mean and/or variance. A real case study, as well as a simulated one, is adjusted to investigate the capability of our proposed chart.