$1$

$2$

$3$

$4$

$5$

$6$

$0\mathrm{.}1261$

$0\mathrm{.}1259$

$0\mathrm{.}1239$

$0\mathrm{.}1225$

$0\mathrm{.}1259$

$0\mathrm{.}1255$

$0\mathrm{.}1253$

$0\mathrm{.}1263$

$0\mathrm{.}1265$

$0\mathrm{.}1249$

$0\mathrm{.}1243$

$0\mathrm{.}1273$

$0\mathrm{.}1245$

$0\mathrm{.}1247$

$0\mathrm{.}126$

$0\mathrm{.}1265$

$0\mathrm{.}1242$

$0\mathrm{.}1245$

$0\mathrm{.}1249$

$0\mathrm{.}124$

$0\mathrm{.}1257$

$0\mathrm{.}1248$

$0\mathrm{.}1257$

$0\mathrm{.}1268$

$0\mathrm{.}1248$

$0\mathrm{.}1251$

$0\mathrm{.}1243$

$0\mathrm{.}1256$

$0\mathrm{.}1251$

$0\mathrm{.}1263$

Time left $0$:$58$:$41$

A small manufacturer of metal ring seals for aircraft engines has been asked by its major customer to implement statistical process control $($SPC$).$ One major type of ring requires cutting a one$-$eighth inch wide slot using a milling machine. The following six samples of five observations each, taken every half hour, are width of the slots $($in inch$)$ made by the milling machine on the rings.

a$)$ Set up the sample mean and range control charts for this operation. $4$

marks

b$)$ Is the process in control? $2$ marks

c$)$ The seventh sample contains the following values: $0\mathrm{.}124,0\mathrm{.}1252,0\mathrm{.}1295,0\mathrm{.}1262,$ and $0\mathrm{.}1275.2$ marks Using the control charts from part $($a$),$ is the process still in control. $2$ marks