Question $7$

A process manager wants to use control charts to control their process. They have decided that each

sample should have $4$ observations. The number of standard deviations the manager wants to use is $3.$

The manager found that the average range of the samples is $5.$ The grand average of the samples is

$6\mathrm{.}0.$ The standard deviation of the observations is $2.$ The manager took $20$ samples to use to calculate

the control limits$.$ The formulas used to calculate the control limits is:

$UC{L}_x=x_{\frac{?}{\text{b}\text{a}\text{r}}\frac{?}{\text{b}\text{a}\text{r}}}+\frac{zs}{\sqrt[\phantom{2}]{n}}$

In this example, UCL$=$

$4$

$6$

$9$

$10$