computed. This yields

${\displaystyle \underset{i=1}{\overset{30}{}}}{\stackrel{}{x}}_i=607\mathrm{.}8$ and ${\displaystyle \underset{i=1}{\overset{30}{}}}{R}_i=144.$

$($a$)$ Compute the center line and control limits for the $\stackrel{}{x}$ and $R$ control charts.

$($b$)$ Suppose both charts exhibit in$-$control. There is a single lower specification limit of $16lb.$ If strength is normally distributed, what fraction of yarn would fail to meet specifications?

$($c$)$ Is the process capable, can you define a $Cp$ for it$?$

$($d$)$ If the process is out of control, can you get its process capability?

$($e$)$ If one can't get process capability in $($d$)$ what one should do to assess process capability? $($please list the detail steps$/$procedure for it$)$