The data in the table below were taken by one operator during a gauge capability study.

$($a$)$ Estimate sigma$-$gauge.

$($b$)$ Determine control chart parameters for the $x-$bar and $R$ charts for this study.

$($c$)$ Suppose USL $=30,$ and $LSL=15,$ use $\frac{P}{T}$ ratio to comment this process.

$\backslash$table$[[$Part$,$Measurements,Part,Measurements$],[,,,,,],[$Number$,1,2,$Number,$1,2],[1,20,20,9,20,20],[2,19,20,10,23,22],[3,21,21,11,28,22],[4,24,20,12,19,25],[5,21,21,13,21,20],[6,25,26,14,20,21],[7,18,17,15,18,18],[8,16,15,,,]]$