The Canine Gourmet Company produces delicious dog treats for canines with discriminating tastes. Management wants the$$ box$-$filling line to be set so that the process average weight per packet is $42$ grams. To make sure that the process is in$$ control, an inspector at the end of the filling line periodically selects a random box of $10$ packets and weighs each packet. When the process is in$$ control, the range in the weight of each sample has averaged $5$ grams.

LOADING... Click the icon to view the table of factors for calculating$$ three$-$sigma limits for the x overbar$-$chart and$$ R$-$chart.

Part $2$

a$.$ Design an$$ R$-$ and an x overbar$-$chart for this process.

The UCL Subscript Upper R equals

$$

$8\mathrm{.}89$ grams and the LCL Subscript Upper R equals

$$

$1\mathrm{.}12$ grams. $($Enter your response rounded to two decimal$$ places.$)$

Part $3$

The UCL Subscript x overbar equals

$$

$43\mathrm{.}54$ grams and the LCL Subscript x overbar equals

$$

$40\mathrm{.}46$ grams. $($Enter your responses rounded to two decimal$$ places.$)$

Part $4$

b$.$ The results from the last $5$ samples of $10$ packets are shown below. Is the process in$$ control? Explain.

$$

Sample

x overbar

R

$1$

$40$

$7$

$2$

$43$

$3$

$3$

$41$

$6$

$4$

$43$

$3$

$5$

$41$

$5$

The process variability is

$$

in

out of

statistical control and the process average is

$$

out of

in

statistical control.$$ Therefore, the entire process is

$$

in

out of

control.The Canine Gourmet Company produces delicious dog treats for canines with discriminating tastes. Management

wants the box$-$filling line to be set so that the process average weight per packet is $42$ grams. To make sure that the

process is in control, an inspector at the end of the filling line periodically selects a random box of $10$ packets and

weighs each packet. When the process is in control, the range in the weight of each sample has averaged $5$ grams.

E Click the icon to view the table of factors for calculating three$-$sigma limits for the $\stackrel{}{x}-$chart and R$-$chart.

a$.$ Design an R$-$ and an $\stackrel{}{x}-$chart for this process.

The $UC{L}_R$ equals grams and the $LC{L}_R$ equals grams. $($Enter your response rounded to two

decimal places.$)$

The $UC{L}_{\stackrel{}{x}}$ equals $43\mathrm{.}54$ grams and the $LC{L}_{\stackrel{}{x}}$ equals grams. $($Enter your responses rounded to two

decimal places.$)$

b$.$ The results from the last $5$ samples of $10$ packets are shown below. Is the process in control? Explain.

The process variability is

statistical control and the process average is

statistical control. Therefore,

the entire process is

control.