A milling operation will be monitored using mean and range charts. Eighteen samples of five items were pulled and measured when the process was in control.

$1$a$.$ Compute the upper and lower control limits for the chart $($round answers to $3$ decimals$).$

$UC{L}_{x-\text{b}\text{a}\text{r}}$

LCLx$-$bar $$

$1$b$.$ Compute the upper and lower control limits for the $R$ chart $($round answers to $3$ decimals$).$

UCL $L_R$

LCL $L_R$