The data shown in the following table $($Table $5)$ are $$x and R values for $24$ samples

of size n $=5$ taken from a process producing bearings. The measurements are made on the

inside diameter of the bearing.

$($a$)$ Set up $$x and R chart limits on this process. Does the process seem to be in statistical

control? If necessary, revise the control limits$.$

$($b$)$ Refer to Table $5.$ Suppose that you wished to continue charting this quality characteristic using $$x and R charts based on a sample size of n $=3.$ What limits would be used

on the $$x and R charts? Consider all $24$ samples.

$($c$)$ What would be the impact of the decision you made in part $($b$)$ on the ability of the

chart to detect a shift in the mean? That is$,$ using n $=3$ instead of n $=5.$