## 6 Results, Discussion, and Findings
* As the values of shift increase for the suggested HEWMA control chart under the Bayesian approach using RSS schemes it rapidly decreases more than the Bayesian HEWMA and Bayesian AEWMA control chart using SRS. For example, Tables 3 and 4 at \(ARL_{0}=370\), \(\lambda_{1}=0.10\), and \(\lambda_{2}=0.25\), the ARL results at \(\sigma=0.30\) is 19.91 and 3.83 at \(\sigma=0.80\) using RSS. They are 16.36 and 3.18 using MRSS, and the ARL values in the same situation using ERSS are 22.06 and 4.31. The results show that the proposed Bayesian control chart is more efficient. * The results are given in Tables 5 and 6 for posterior and posterior predictive distribution under LLF using informative prior, the values of ARL at \(ARL_{0}=370\), \(\sigma=20\), \(\lambda_{1}=0.10\), and \(\lambda_{2}=0.05\) are 37.38 and at the ARL value, the result is 40.61 utilizing RSS. the ARL values for the same case using MRSS are 25.15 and 33.61. For ERSS, the ARL values are 40.76 and 46.01, which shows that the results presented in Tables 3-6 for posterior distribution under LLF are almost the same as the posterior and posterior predictive distribution under LLF. \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 HEWMA**} & \multicolumn{2}{c}{**Bayesian**} & \multicolumn{2}{c}{**Bayesian**} \\  & \multicolumn{2}{c}{**SRS**} & \multicolumn{2}{c}{**AEWMA SRS**} & \multicolumn{2}{c}{**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}{**\(L\) = 2.099**} & \multicolumn{2}{c}{**\(h\) = 0.0856**} & \multicolumn{2}{c}{**\(L\) = 2.085**} & \multicolumn{2}{c}{**\(L\) = 2.081**} & \multicolumn{2}{c}{**\(L\) = 2.0864**} \\ \hline
0.00 & 371.67 & 408.54 & 370.86 & 537.77 & 370.17 & 409.83 & 368.36 & 425.51 & 3  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Bayesian HEWMA**} & \multicolumn{2}{c}{**Bayesian**} & \multicolumn{2}{c}{**Bayesian HEWMA**} & \multicolumn{2}{c}{**Bayesian**} & \multicolumn{2}{c}{**Bayesian**} \\ \cline{2-11}
**Shift** & \multicolumn{2}{c}{**SRS**} & \multicolumn{2}{c}{**AEWMA SRS**} & \multicolumn{2}{c}{**RSS**} & \multicolumn{2}{c}{**AEWMA MRSS**} & \multicolumn{2}{c}{**HEWMA MRSS**} & \multicolumn{2}{c}{**HEWMA ERSS**} \\ \cline{2-11}  & \multicolumn{2}{c}{**ARL**} & **SDRL** & **ARL** & **SDRL** & **ARL** & **ARL** & **SDRL** & **ARL** & **SDRL** & **ARL** \\ \cline{2-11}  & \multicolumn{2}{c}{**_L_ **= 2.2709**} & \multicolumn{2}{c}{_h_ **= 0.241**} & \multicolumn{2}{c}{_L_ **= 2.2656**} & \multicolumn{2}{c}{_L_ **= 2.2644**} & \multicolumn{2}{c}{_L_ **= 2.2654**} \\ \hline
0.00 & 370.10 & 389.87 & 3  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Bayesian HEWMA**} & \multicolumn{2}{c}{**Bayesian**} & \multicolumn{2}{c}{**Bayesian**} & \multicolumn{2}{c}{**Bayesian**} & \multicolumn{2}{c}{**Bayesian**} \\ \cline{2-11}
**Shift** & \multicolumn{2}{c}{**SRS**} & \multicolumn{2}{c}{**AEWMA SRS**} & \multicolumn{2}{c}{**HEWMA RSS**} & \multicolumn{2}{c}{**HEWMA MRSS**} & \multicolumn{2}{c}{**HEWMA MRSS**} & \multicolumn{2}{c}{**HEWMA ERSS**} \\ \cline{2-11}  & \multicolumn{2}{c}{**ARL**} & **SDRL** & **ARL** & **SDRL** & **ARL** & **ARL** & **SDRL** & **ARL** & **SDRL** & **ARL** \\ \cline{2-11}  & \multicolumn{2}{c}{**_L_ = 2.2716**} & \multicolumn{2}{c}{_h_ = 0.242} & \multicolumn{2}{c}{_L_ = 2.2777**} & \multicolumn{2}{c}{_L_ = 2.2644**} & \multicolumn{2}{c}{_L_ = 2.2785**} \\ \hline
0.00 & 371.51 & 399.34 & 370.14 & 434.88 & 370.33 & 413.48 & 3  
Tables 1-6 present the results of the suggested Bayesian HEWMA control chart under RSS schemes for posterior and posterior predictive distribution by using informative prior, and utilizing both LFs, i.e., SELF and LLF.