Sampling

$44$

pieces of$$ precision$-$cut wire$($to be used in computer$$ assembly$)$ every hour for the past $24$ hours has produced the following$$ results:

$$

Hour

Bold x overbarx

R

Hour

Bold x overbarx

R

Hour

Bold x overbarx

R

Hour

Bold x overbarx

R

$1$

$3\mathrm{.}253\mathrm{.}25"$

$0\mathrm{.}760\mathrm{.}76"$

$7$

$3\mathrm{.}153\mathrm{.}15"$

$0\mathrm{.}580\mathrm{.}58"$

$13$

$3\mathrm{.}113\mathrm{.}11"$

$0\mathrm{.}850\mathrm{.}85"$

$19$

$3\mathrm{.}413\mathrm{.}41"$

$1\mathrm{.}661\mathrm{.}66"$

$2$

$3\mathrm{.}203\mathrm{.}20$

$1\mathrm{.}181\mathrm{.}18$

$8$

$2\mathrm{.}752\mathrm{.}75$

$1\mathrm{.}081\mathrm{.}08$

$14$

$2\mathrm{.}832\mathrm{.}83$

$1\mathrm{.}361\mathrm{.}36$

$20$

$2\mathrm{.}992\mathrm{.}99$

$1\mathrm{.}091\mathrm{.}09$

$3$

$3\mathrm{.}323\mathrm{.}32$

$1\mathrm{.}381\mathrm{.}38$

$9$

$2\mathrm{.}922\mathrm{.}92$

$0\mathrm{.}710\mathrm{.}71$

$15$

$3\mathrm{.}023\mathrm{.}02$

$1\mathrm{.}011\mathrm{.}01$

$21$

$2\mathrm{.}752\mathrm{.}75$

$1\mathrm{.}031\mathrm{.}03$

$4$

$3\mathrm{.}493\mathrm{.}49$

$1\mathrm{.}311\mathrm{.}31$

$10$

$2\mathrm{.}752\mathrm{.}75$

$1\mathrm{.}381\mathrm{.}38$

$16$

$2\mathrm{.}942\mathrm{.}94$

$0\mathrm{.}550\mathrm{.}55$

$22$

$3\mathrm{.}383\mathrm{.}38$

$0\mathrm{.}460\mathrm{.}46$

$5$

$3\mathrm{.}173\mathrm{.}17$

$1\mathrm{.}221\mathrm{.}22$

$11$

$2\mathrm{.}832\mathrm{.}83$

$1\mathrm{.}221\mathrm{.}22$

$17$

$2\mathrm{.}962\mathrm{.}96$

$1\mathrm{.}481\mathrm{.}48$

$23$

$3\mathrm{.}043\mathrm{.}04$

$1\mathrm{.}581\mathrm{.}58$

$6$

$2\mathrm{.}962\mathrm{.}96$

$0\mathrm{.}320\mathrm{.}32$

$12$

$3\mathrm{.}073\mathrm{.}07$

$0\mathrm{.}350\mathrm{.}35$

$18$

$2\mathrm{.}642\mathrm{.}64$

$1\mathrm{.}241\mathrm{.}24$

$24$

$2\mathrm{.}642\mathrm{.}64$

$1\mathrm{.}021\mathrm{.}02$

Based on the sampling$$ done,

the

control limits for $3-$sigma

x overbarx

chart are $($round all intermediate calculations to three decimal places before proceeding with further

$$calculations$)$:

Part $2$

Upper Control Limit

$($UCL Subscript x overbarUCLx$)$

$=$

enter your response here

inches $($round your response to three decimal$$ places$).$

Part $3$

Lower Control Limit

$($LCL Subscript x overbarLCLx$)$

$=$

enter your response here

inches $($round your response to three decimal$$ places$).$

Part $4$

Based on the

x overbarx$-$chart,

the wire cutting process has been

$$

$$

IN CONTROL

OUT OF CONTROL

$.$

Part $5$

The control limits for the

$3-$sigma

$$ R$-$chart are $($round all intermediate calculations to three decimal places before proceeding with further

$$calculations$)$:

Part $6$

Upper Control Limit

$($UCL Subscript Upper RUCLR$)$

$=$

enter your response here

inches $($round your response to three decimal$$ places$).$

Part $7$

Lower Control Limit

$($LCL Subscript Upper RLCLR$)$

$=$

enter your response here

inches $($round your response to three decimal$$ places$).$

Part $8$

Based on the$$ R$-$chart, the wire cutting process has been

$$

$$

IN CONTROL

OUT OF CONTROL

$.$