Problem $2$ The data shown below for $3$ samples are taken from a process producing steel shafts. The measurements are made on the length of the shafts. The shaft length has an engineering specification of

$11\backslash$pm $3$

feet. a$)$ Estimate the process mean and standard deviation. b$)$ Set up

x

$-$bar and

R

charts on this process. Does the process seem to be in statistical control? c$)$ Calculate the capability index

$($C

P

$$

$)$

for this process. d$)$ Calculate the capability index

$($C

pu

$$

$)$

for this process. e$)$ Calculate the expected percentage above the upper spec limit $($USI$).$ f$)$ Calculate the expected pereentage below the lower spec limit $($ISL$).$