: A process is in statistical control with x$=39\mathrm{.}7$ and R $=2\mathrm{.}5.$ The control chart uses a sample size of n$=2.$

Specifications are at $40\backslash$pm $5.$ The quality characteristic is normally distributed.

$($a$)$ Estimate the potential capability of the process $($

$$

Cp

$).$

$($b$)$ Estimate the actual process capability

$$

$(,)$ C C C pk pl pu

$.$

$($c$)$ Calculate and compare the PCRs

$$

$()$ C and C pm pkm

$.$

Note:

$,,$

T $=$ Target of the process