$6\mathrm{.}24.$ Consider the $x$ and $R$ chart that you established in Exercise $6\mathrm{.}15$ for the piston ring process. Suppose that you want to continue control charting piston ring diameter using $n=3.$ What limits would be used on the $\stackrel{}{x}$ and $R$ chart?

$6\mathrm{.}15.$ Consider the piston ring data shown in Table $6\mathrm{.}3.$ Assume that the specifications on this component are $74\mathrm{.}000+0\mathrm{.}05mm.$

$($a$)$ Set up $\stackrel{}{x}$ and $R$ control charts on this process. Is the process in statistical control?

$($b$)$ Note that the control limits on the $\stackrel{}{x}$ chart in part $($a$)$ are identical to the control limits on the $\stackrel{}{x}$ chart in Example $6\mathrm{.}3,$ where the limits were based on $s.$ Will this always happen?

$($c$)$ Estimate process capability for the piston$-$ring process. Estimate the percentage of piston rings produced that will be outside of the specification.