Sampling $4$ 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 overbar $($cm$)$

R$($cm$)$

Hour

Bold x overbar $($cm$)$

R$($cm$)$

Hour

Bold x overbar $($cm$)$

R$($cm$)$

Hour

Bold x overbar $($cm$)$

R$($cm$)$

$1$

$3\mathrm{.}15$

$0\mathrm{.}71$

$7$

$3\mathrm{.}15$

$0\mathrm{.}53$

$13$

$3\mathrm{.}11$

$0\mathrm{.}80$

$19$

$4\mathrm{.}51$

$1\mathrm{.}66$

$2$

$3\mathrm{.}10$

$1\mathrm{.}18$

$8$

$2\mathrm{.}55$

$1\mathrm{.}13$

$14$

$2\mathrm{.}93$

$1\mathrm{.}26$

$20$

$2\mathrm{.}89$

$1\mathrm{.}04$

$3$

$3\mathrm{.}32$

$1\mathrm{.}48$

$9$

$3\mathrm{.}12$

$0\mathrm{.}71$

$15$

$3\mathrm{.}22$

$1\mathrm{.}01$

$21$

$2\mathrm{.}65$

$1\mathrm{.}13$

$4$

$3\mathrm{.}49$

$1\mathrm{.}31$

$10$

$2\mathrm{.}85$

$1\mathrm{.}28$

$16$

$2\mathrm{.}94$

$0\mathrm{.}45$

$22$

$3\mathrm{.}38$

$0\mathrm{.}46$

$5$

$3\mathrm{.}07$

$1\mathrm{.}22$

$11$

$2\mathrm{.}83$

$1\mathrm{.}17$

$17$

$2\mathrm{.}96$

$1\mathrm{.}48$

$23$

$3\mathrm{.}04$

$1\mathrm{.}58$

$6$

$2\mathrm{.}86$

$0\mathrm{.}37$

$12$

$2\mathrm{.}97$

$0\mathrm{.}40$

$18$

$2\mathrm{.}64$

$1\mathrm{.}24$

$24$

$2\mathrm{.}74$

$1\mathrm{.}02$

Develop appropriate control charts and determine whether there is any cause for concern in the cutting process. Plot the information and look for patterns.

LOADING... Click the icon to view the table of control chart constants Upper A $2,$ Upper D $4,$ Upper D $3.$

Based on the sampling$$ done, the control limits for $3-$sigma x overbar chart are $($round all intermediate calculations to three decimal places before proceeding with further $$calculations$)$:

Part $2$

Upper Control Limit $($UCL Subscript x overbar$)$equals

$$

enter your response here cm $($round your response to three decimal$$ places$).$

Part $3$

Lower Control Limit $($LCL Subscript x overbar$)$equals

$$

enter your response here cm $($round your response to three decimal$$ places$).$