Consider a process which, when in control, has $\frac{?}{\text{b}\text{a}\text{r}}(\stackrel{}{x})=500$ and $=25.$

$($a$)$ Determine the $\stackrel{}{x}$ and $R$ control chart limits if $n=4.$

$($b$)$ Determine the $\stackrel{}{x}$ and $R$ control chart limits if $n=9.$

$($c$)$ Determine the $\stackrel{}{x}$ and $R$ control chan limits if $n=2.$

$($d$)$ Suppose that a shift in process centering occurred from $\frac{?}{\text{b}\text{a}\text{r}}(\stackrel{}{x})=500$ to $530.$ Which

subgroup size above yields an $\stackrel{}{x}$ chart that is best capable of detecting the shift?

Why? What is the major disadvantage of using that sample size?