Frozen orange juice concentrate is packed in $6-$oz cardboard cans. These cans are formed on a machine by spinning them from cardboard stock and attaching a metal bottom panel. By inspection of a can, we may determine whether, when filled, it could possibly leak either on the side seam or around the bottom joint. Such a nonconformance can have an improper seal on either the side seam or the bottom panel. Establish statistical process control of this process. Process manager collects $30$ samples first to understand the process.

Sample Number Nonconforming Cans Fraction defective

$1120\mathrm{.}24$

$2150\mathrm{.}3$

$380\mathrm{.}16$

$4100\mathrm{.}2$

$540\mathrm{.}08$

$670\mathrm{.}14$

$7160\mathrm{.}32$

$890\mathrm{.}18$

$9140\mathrm{.}28$

$10100\mathrm{.}2$

$1150\mathrm{.}1$

$1260\mathrm{.}12$

$13170\mathrm{.}34$

$14120\mathrm{.}24$

$15220\mathrm{.}44$

$1680\mathrm{.}16$

$17100\mathrm{.}2$

$1850\mathrm{.}1$

$19130\mathrm{.}26$

$20110\mathrm{.}22$

$21200\mathrm{.}4$

$22180\mathrm{.}36$

$23240\mathrm{.}48$

$24150\mathrm{.}3$

$2590\mathrm{.}18$

$26120\mathrm{.}24$

$2770\mathrm{.}14$

$28130\mathrm{.}26$

$2990\mathrm{.}18$

$3060\mathrm{.}12$

Control limits are established with the above data after establishing process control. The manager collects a few more samples to see if the process is further remaining under control.

$3190\mathrm{.}18$

$3260\mathrm{.}12$

$33120\mathrm{.}24$

$3450\mathrm{.}1$

$3560\mathrm{.}12$

$3640\mathrm{.}08$

$3760\mathrm{.}12$

$3830\mathrm{.}06$

$3970\mathrm{.}14$

$4060\mathrm{.}12$

$4120\mathrm{.}04$

$4240\mathrm{.}08$

$4330\mathrm{.}06$

$4460\mathrm{.}12$

$4550\mathrm{.}1$

$4640\mathrm{.}08$

$4780\mathrm{.}16$

$4850\mathrm{.}1$

$4960\mathrm{.}12$

$5070\mathrm{.}14$

$5150\mathrm{.}1$

$5260\mathrm{.}12$

$5330\mathrm{.}06$

$5450\mathrm{.}1$

Prepare analysis based on the above data.Frozen orange juice concentrate is packed in $6-$oz cardboard cans. These cans are formed on a

machine by spinning them from cardboard stock and attaching a metal bottom panel. By inspection

of a can, we may determine whether, when filled, it could possibly leak either on the side seam or

around the bottom joint. Such a nonconformance can have an improper seal on either the side seam

or the bottom panel. Establish statistical process control of this process. Process manager collects

$30$ samples first to understand the process.