Ch$.10$: Quality Control: Means and Ranges Control Limits $(5$ pts$)-$ Jensen Machine Shop

Jensen Machine Shop is evaluating times $($in minutes$)$ to setup its main machine. Samples of five observations have been taken and the results are provided below.

a$.$ b$.$

Use the factors ni the attached table to calculate control limits for means and for ranges. Is the process in control and why? sI the process out of control and why? Be specific.

$12$

$81\mathrm{.}179\mathrm{.}2$

$80\mathrm{.}0078\mathrm{.}880\mathrm{.}580.080\mathrm{.}678\mathrm{.}4$

$79\mathrm{.}781\mathrm{.}0$

Sample $3456$

Numberor Observations ni Sample:

Factor for chart

lower controle, L i m i t y

D$.0$

Uppercontrol P L I mi

$3\mathrm{.}27$

TABLE $3\mathrm{.}01$

Factors for three$-$sigma control limits ofr Xand R charts

Source: Adapted from LegeGnreant

$2$

$1\mathrm{.}881\mathrm{.}02.0\mathrm{.}735$

$0\mathrm{.}58$ G

$0\mathrm{.}4870\mathrm{.}42$

$8$

$0\mathrm{.}379$

$0\mathrm{.}3410$

$0\mathrm{.}311$

$0\mathrm{.}2912.$

$0\mathrm{.}2713$

$0\mathrm{.}25140\mathrm{.}2415$

$0\mathrm{.}221$

$16$

$0\mathrm{.}2117$

$0\mathrm{.}2018$

$0\mathrm{.}1919$

$0.19200\mathrm{.}18$

$2\mathrm{.}5702\mathrm{.}282\mathrm{.}112\mathrm{.}000\mathrm{.}08$

$1\mathrm{.}9201.$

$18\mathrm{.}601\mathrm{.}8$

$18\mathrm{.}202\mathrm{.}2$

$17\mathrm{.}802\mathrm{.}6$

$17\mathrm{.}102\mathrm{.}8$

$17\mathrm{.}203\mathrm{.}1$

$16\mathrm{.}90\mathrm{.}33$

$16\mathrm{.}70\mathrm{.}35$

$16\mathrm{.}50\mathrm{.}36$

$1\mathrm{.}640\mathrm{.}38$

$16\mathrm{.}20\mathrm{.}39$

$16\mathrm{.}10\mathrm{.}40$

$16.00\mathrm{.}41$

$15\mathrm{.}9$