## 7 Real Data Applications  
Inside the SPC literature, a standard exercise that has been used by many analysts is to clarify the execution and overall performance of the control charts using actual and simulated datasets. In this article, we use a real dataset to explain the work and execution of the proposed Bayesian AEWMA control chart under different RSS schemes utilizing two different LFs for posterior and posterior predictive distribution. The dataset is taken from Montgomery [26], which includes 45 samples, each of size 5 wafers. In semiconductor manufacturing, conjunction with photolithography is used with the hard-bake process. For measurement of the flow width microns are used, and a one hour time interval is taken between the samples. Consider the initial 30 samples from the in-control process (phase-I), while the remaining 15 samples from the out-of-control process (phase-II). Moreover, all the observation in the phase-II dataset is obtained by adding 0.017, which shows an ascending shift in the core process mean.  
The HEWMA and AEWMA control charts under the Bayesian approach based on SRS by using SELF for posterior and posterior predictive distribution are shown in Figures 1 and 2, respectively, which indicates that the process is out-of-control on the 42 nd and 40 th samples, respectively. Figures 2-4 show the proposed Bayesian HEWMA control chart using SELF based on RSS schemes for posterior and posterior predictive distribution, the process shows out-of-control signals on the 36 th, 35 th, and 37 th sample for RSS, MRSS, and ERSS, respectively. Based on Figures 1-5, the suggested Bayesian HEWMA control charts using RSS schemes are more sensitive in detecting out-of-control signals than the Bayesian HEWMA and Bayesian AEWMA control charts using SRS.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Shift**} & \multicolumn{2}{c}{**Bayesian HEWMA**} & \multicolumn{2}{c}{**Bayesian**} & \multicolumn{2}{c}{**Bayesian**} & \multicolumn{2}{c}{**Bayesian**} & \multicolumn{2}{c}{**Bayesian**} \\  & \multicolumn{2}{c}{**SRS**} & \multicolumn{2}{c}{**AEWMA SRS**} & \multicolumn{2}{c}{**HEWMA RSS**} & \multicolumn{2}{c}{**HEWMA MRSS**} & \multicolumn{2}{c}{**HEWMA ERSS**} \\ \cline{2-10}  & **ARL** & **SDRL** & **ARL** & **SDRL** & **ARL** & **SDRL** & **ARL** & **SDRL** & **ARL** & **SDRL** \\ \cline{2-10}  & \multicolumn{2}{c}{**L = 2.2717**} & \multicolumn{2}{c}{**_h = 0.2414_} & \multicolumn{2}{c}{**_L = 2.2771_} & \multicolumn{2}{c}{**_L = 2.2649_} & \multicolumn{2}{c}{**_L = 2.2781_} \\ \hline
0.00 & 372.35 & 391.96 & 368.67 & 359.45 & 380.12 & 396.83 & 369.24 & 386.76 & 368.89 & 436.27 \\
0.10 & 206.32 & 211.24 & 210.29 & 197.72 & 112.72 & 122.32 & 100.70 & 99.31 & 130.03 & 128.34 \\
0.20 & 90.30 & 86.01 & 98.16 & 83.24 & 40.61 & 34.92 & 33.61 & 28.40 &  
Figure 1: Bayesian HEWMA control chart using posterior and posterior predictive distribution under SELF for SRS.  
Figure 2: Bayesian AEWMA control chart using posterior and posterior predictive distribution under SELF for SRS.  
Figure 4: Bayesian HEWMA control chart using posterior and posterior predictive distribution under SELF for MRSS.  
Figure 3: Bayesian HEWMA control chart using posterior and posterior predictive distribution under SELF for RSS.