# An Enhanced Auxiliary Information-Based EWMA-t Chart for Monitoring the Process Mean
## 6 Conclusions  
EWMA-t and AIB-EWMA-t charts are effective for monitoring changes in the process mean when the process standard deviation is unstable or poorly estimated. To enhance the detection ability, this study combines the features of the GWMA chart to propose GWMA-t and AIB-GWMA-t charts to monitor small process mean shifts. The EWMA-t, GWMA-t, and AIB-EWMA-t charts are special cases of the AIB-GWMA-t chart. Performance comparisons of the proposed AIB-GWMA-t charts are evaluated using the \(ARL\) indicator. The numerical simulations indicate that the AIB-GWMA-t chart performs substantially better than its reduced cases such as the AIB-EWMA-t, GWMA-t, and EWMA-t charts in detecting small shifts in the process mean. Moreover, the simulation also recommends that when the auxiliary variable is related to the quality characteristic between \(\rho=0.25\) and \(\rho=0.75\), the AIB-GWMA-t chart with large values (\(q=0.95\) and \(\alpha=0.9\)) is a suitable alternative. Even with a high correlation coefficient \(\rho=0.95\), the AIB-GWMA-t chart with large \(q\) and \(\alpha\) performs comparable to the AIB-EWMA-t chart. Finally, an example is provided to illustrate the implementation of our proposed AIB-GWMA-t chart as well as its reduced charts. Conceptualization, J.-H.C.; methodology, S.-L.L. ; software, J.-H.C.; validation, J.-H.C. and S.-L.L. ; formal analysis, S.-L.L. ; investigation, J.-H.C. and S.-L.L. ; writing--original draft preparation, S.-L.L. ; writing--review and editing, J.-H.C. All authors have read and agreed to the published version of the manuscript. This research received no external funding. The authors declare no conflict of interest. The algorithmic description of the AIB-GWMA-t chart. The following questions are:  
1. [label=]
2. The AIB-EWMA-t chart is a \(\rho=0.00,0.25,0.50,0.75,0.95\)
3. The AIB-EWMA-t chart is a \(\rho=0.5,0.7,0.9,0.95\)
4. The AIB-EWMA-t chart is a \(\rho=0.1,0.2,0.4,0.6,1  
+++ ==WARNING: Truncated because of repetitions==
.0,2.0\)  
++  
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