The data shown in the table below are $$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, with only the last three decimals recorded $($i$.$e$.,34\mathrm{.}5$ should be $0\mathrm{.}50345).$

Perform a process capability analysis using $$and R charts for the data shown in the table

below.

Note that $$

$$

$2$

Show how each of the following capability indices are calculated:

$($a$)$ Cp

$($b$)$ Cpu $($note: $=$

USL$$

$3$

$)$

$($c$)$ Cpl $($note: Cpl $=$

$$LSL

$3$

$)$

$($d$)$ Cpk