Problem $1(16$ pts$.).$

It is required to establish Upper and Lower Quality Control limits on the weight of a

semolina product produced in a Flour Mills Factory. $12$ samples of size $5$ are taken and

the following Average Weight values $($grams$)$ as well as Range values $($Maximum$-$

Minimum$)$ are determined for each sample.

a$)$ Establish $30$ control limits for $x$ and $R$ charts to be used for fintere process control.

$($Note: Delete the points that are out of control limits and reestablish the limits$)$

b$)$ If the specifications are $75+-3$ grams on the product weight, what would be process

capability? What do you think of these specifications as related to the process itself?

c$)$ If the sample size of $5$ is reduced to $3,$ what would be the new control limits for the $\stackrel{}{x}$

chart?

d$)$ What would be the control limits for $n=5$ and type I error of $a=0\mathrm{.}005$ for the same

data above?