How do you compute utilization knowing Actual Output and Maximum Capacity?

What would be the Upper and Lower Control Limits for both a Range Chart and a Mean Chart based on

the following samples?

Sample

$1$

Sample

$2$

Sample

$3$

Sample

$4$

Sample

$5$

$43\mathrm{.}9043\mathrm{.}8044\mathrm{.}1043\mathrm{.}2043\mathrm{.}20$

$43\mathrm{.}9043\mathrm{.}6042\mathrm{.}1044\mathrm{.}5046\mathrm{.}50$

$41\mathrm{.}1042\mathrm{.}1044\mathrm{.}3042\mathrm{.}3044\mathrm{.}50$

$42\mathrm{.}2042\mathrm{.}5041\mathrm{.}9041\mathrm{.}2042\mathrm{.}00$

$43\mathrm{.}1043\mathrm{.}1044\mathrm{.}3041\mathrm{.}9043\mathrm{.}10$

Please use this chart as a reference.

Answer

X UCL $44\mathrm{.}57$

LCL $41\mathrm{.}71$

R UCL $5\mathrm{.}2452$

LCL $0$

Size of Factor for UCL and LCL forFactor for Factor for

Sample x$-$bar$-$ChartsLCL for UCL for

A$2$ R$-$Charts R$-$Charts

D$3$ D$4$

$21\mathrm{.}8803\mathrm{.}267$

$31\mathrm{.}02302\mathrm{.}575$

$40\mathrm{.}72902\mathrm{.}282$

$50\mathrm{.}57702\mathrm{.}115$

$60\mathrm{.}48302\mathrm{.}004$

$70\mathrm{.}4190\mathrm{.}0761\mathrm{.}924$

$80\mathrm{.}3730\mathrm{.}1361\mathrm{.}864$

$90\mathrm{.}3370\mathrm{.}1841\mathrm{.}816$

$100\mathrm{.}3080\mathrm{.}2231\mathrm{.}777$