Question $1$

and R$-$chart

a$)$ The sample size is

b$)$ The center line for $\backslash ($ x $\backslash )-$chart is

d$)$ The center line for R$-$chart is

e$)$ For $\backslash ($ x $\backslash )-$chart, the UCL is

and $\backslash ($ L C L $\backslash )$ is

f$)$ For R$-$chart, the UCL i:

and LCLi

g$)$ If the true diameter mean should be $155$ mm and this is your center line, the new UCL is and LCL is