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 bottle neck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions $($in inches$)$ from the last six samples are:

Bottles

Sample

$1$

$2$

$3$

$4$

$1$

$0\mathrm{.}594$

$0\mathrm{.}622$

$0\mathrm{.}598$

$0\mathrm{.}590$

$2$

$0\mathrm{.}587$

$0\mathrm{.}611$

$0\mathrm{.}597$

$0\mathrm{.}613$

$3$

$0\mathrm{.}571$

$0\mathrm{.}580$

$0\mathrm{.}595$

$0\mathrm{.}602$

$4$

$0\mathrm{.}610$

$0\mathrm{.}615$

$0\mathrm{.}585$

$0\mathrm{.}578$

$5$

$0\mathrm{.}580$

$0\mathrm{.}624$

$0\mathrm{.}618$

$0\mathrm{.}614$

$6$

$0\mathrm{.}585$

$0\mathrm{.}593$

$0\mathrm{.}607$

$0\mathrm{.}569$

Requirements:

Assume that only these six samples are sufficient, and use the data to determine control limits for $($a$)$ an R$-$chart, and $($b$)$ an x$-$bar$-$chart