# An Enhanced Auxiliary Information-Based EWMA-t Chart for Monitoring the Process Mean  
[PERSON]  
1 Department of Information Management, Shih Chien University Kaohsiung Campus, Kaohsiung City 845, Taiwan; [EMAIL_ADDRESS]  
2  
[PERSON]  
More recently, significant attempts have been made to develop auxiliary information-based (AIB) charts to enhance the detection ability when auxiliary information is lacking. The plotting statistics of AIB charts are mainly based on parameter estimators estimated from the study variable (quality characteristic) along with one or more correlated auxiliary variables. AIB mean estimators such as classical ratio, product, and regression estimators are more accurate than those estimated only using the study variable. The advantages of accurate estimators have encouraged many authors to investigate the designs of AIB charts. [PERSON] [17] first proposed the AIB-Shewhart chart based on regression estimators and showed that it is more sensitive than the classic Shewhart mean chart for monitoring the process mean. [PERSON] et al. [18] and [PERSON] [19] proposed AIB-Shewhart charts using ratio-type and location estimators, respectively. For monitoring small process mean shifts, [PERSON] et al. [20] proposed the AIB-EWMA chart and showed that it outperforms both the classical EWMA chart and the AIB-Shewhart chart. [PERSON] and [PERSON] [21] further enhanced the sensitivity of the AIB-EWMA chart by developing the AIB-GWMA chart for effectively monitoring the process mean and indicated that existing AIB-Shewhart and AIB-EWMA charts are special cases of the proposed chart. The EWMA-type and GWMA-type charts mentioned above use the sample mean to monitor process mean shifts. A practical issue is that an out-of-control signal detection is caused by a change in the process standard deviation instead of process mean shifts. To overcome this problem, [PERSON] et al. [22] proposed using EWMA-t charts to monitor the process mean, finding them to be robust against changes in the process standard deviation compared with EWMA mean charts despite being less sensitive. [PERSON] et al. [23] utilized an EWMA-t chart to monitor the process mean in the short run and showed that it can quickly detect an out-of-control signal. Thereafter, [PERSON] et al. [24] investigated the performance of Shewhart-t, EWMA-t, and CUSUM-t charts for short production runs with an unknown shift size of the process mean. Recently, [PERSON] et al. [25] extended the work of [PERSON] et al. [22] and [PERSON] et al. [20] to propose an AIB-EWMA-t chart for monitoring the process mean when the process standard deviation is unstable. They showed that the AIB-EWMA-t chart not only outperforms the existing EWMA-t chart but also can replace the AIB-EWMA mean chart when the process standard deviation has changed. This study aims to enhance the sensitivity of two types of EWMA-t charts, namely the GWMA-t chart and AIB-GWMA-t chart, to efficiently monitor small process mean shifts when the process standard deviation is unstable. Existing EWMA-t and AIB-EWMA-t charts are special cases of the AIB-GWMA-t chart. The potential limits of the proposed AIB-GWMA-t chart such as single auxiliary variable is considered and correlated to the study variable. Also we assume that two variables follow a bivariate normal distribution with known population means, variances, and correlation coefficient. The Monte Carlo numerical simulations are evaluated using the run length profiles, specifically the average run length (\(ARL\)). A comprehensive comparative study shows that the AIB-GWMA-t chart not only improves the detection ability of the GWMA-t chart, but also surpasses that of the competitive AIB-EWMA-t chart. The organization of the rest of the paper is as follows. Section 2 reviews the EWMA-t and AIB-EWMA-t charts. Section 3 proposes the GWMA-t and AIB-GWMA-t charts. Section 4 evaluates the performance of the GWMA-t and AIB-GWMA-t charts in terms of their \(ARL\) values.