Consider the piston ring data shown in Hole Diameter Data for Exercise $6\mathrm{.}3$

$\backslash$table$[[$Sample$,,,,,],[$Number$,x_1,x_2,x_3,x_4,x_5$Table $6\mathrm{.}3.$ Assume that the specifications on this

component are $74\mathrm{.}000+0\mathrm{.}05mm.$

$($a$)$ Set up and $R$ control charts on this process. Is the process in statistical control?

$($b$)$ Note that the control limits on the chart in part

$($a$)$ are identical to the control limits on the 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.