$1.$ Control Charts $(5$ points$)$

Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of the bottleneck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions$($in$.)$ from the last six samples are

$\backslash$begin$\{$tabular$\}\{$ccccc$\}$

$\backslash$multicolumn$\{5\}\{$c$\}\{$ Bottle $\}\backslash \backslash$

$\backslash$hline Sample & $\backslash (\backslash$mathbf$\{1\}\backslash )$ & $\backslash (\backslash$mathbf$\{2\}\backslash )$ & $\backslash (\backslash$mathbf$\{3\}\backslash )$ & $\backslash (\backslash$mathbf$\{4\}\backslash )\backslash \backslash$

$\backslash$hline $1$ & $0\mathrm{.}589$ & $0\mathrm{.}577$ & $0\mathrm{.}597$ & $0\mathrm{.}583\backslash \backslash$

$2$ & $0\mathrm{.}577$ & $0\mathrm{.}615$ & $0\mathrm{.}620$ & $0\mathrm{.}593\backslash \backslash$

$3$ & $0\mathrm{.}611$ & $0\mathrm{.}624$ & $0\mathrm{.}615$ & $0\mathrm{.}585\backslash \backslash$

$4$ & $0\mathrm{.}584$ & $0\mathrm{.}608$ & $0\mathrm{.}622$ & $0\mathrm{.}612\backslash \backslash$

$5$ & $0\mathrm{.}618$ & $0\mathrm{.}602$ & $0\mathrm{.}596$ & $0\mathrm{.}621\backslash \backslash$

$6$ & $0\mathrm{.}571$ & $0\mathrm{.}612$ & $0\mathrm{.}599$ & $0\mathrm{.}587\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Please calculate the limits for both R$-$chart and $\backslash (\backslash$overline$\{\backslash$mathrm$\{$x$\}\}\backslash )-$ chart and draw them, is this process in control?