c$-$: Answer the following question. Show your calculations. $[$a$-8,$ b $6,$ c $6,$ d$-6$; $26$ points$)$

Thirty samples each of size $7$ have been collected to establish control over a process. The following data were collected:

n

$30$

$\%,=3000$ ;

$)$ R$,=180$

a$.$ Calculate trial control limits for the two charts.

b$.$ On the assumption that the R chart is in control, estimate the process mean and standard $6$

deviation.

c$.$ If we recorded an average of $105$ for sample $31,$ should any special action be taken? Should we revise the control limits$?$

d$.$ Suppose an $\text{'}$S chart were desired. What would be the appropriate control limits and center $6$

line?

$)=3$