Designing an efficient adaptive EWMA model for normal process with engineering applications

Stability in process parameters is required to ensure the quality of the finished item. Control charts, as one of the critical parts of statistical process monitoring ($\mathrm{SPM}$), have seen widespread use across many disciplines for detecting and responding to shifts in process parameters. The adaptive $\mathrm{EWMA}$ ($\mathrm{AEWMA}$) control chart is a well-known scheme that detects both small and large process shifts by integrating the features of the Shewhart and classical $\mathrm{EWMA}$ charts. In this study, we propose an enhanced $\mathrm{AEWMA}$ chart, termed the $\mathrm{EAEWMA}$ chart, that efficiently monitors small and large process mean shifts simultaneously. The proposed $EAEWMA$ chart enhances the existing $\mathrm{AEWMA}$ chart using the shift estimator, based on the hybrid $\mathrm{EWMA}$ ($\mathrm{HEWMA}$) statistic. The Monte Carlo simulation approach is employed as the computational method to obtain the numerical findings for the various performance metrics. The $EAEWMA$ chart is compared with various existing charts, including $AEWMA$, $HEWMA$, $EWMA$, $ACSUM$, and $IACCUSUM$, in zero- and steady-state scenarios. Conclusively, two practical applications of the $\mathrm{EAEWMA}$ chart are presented, demonstrating its value for practitioners and engineers and illustrating its efficacy in real-world scenarios.