rocess average weight per packet is $43$ grams. To make sure that the process is in$$ control, an inspector at the end of the filling line periodically selects a random box of $7$ packets and weighs each packet. When the process is in$$ 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

$$

$9\mathrm{.}62$ grams and the LCL Subscript Upper R equals

$$

$0\mathrm{.}38$ grams. $($Enter your response rounded to two decimal$$ places.$)$

Part $3$

The UCL Subscript x overbar equals

$$

$45\mathrm{.}10$ grams and the LCL Subscript x overbar equals

$$

$40\mathrm{.}91$ grams. $($Enter your responses rounded to two decimal$$ places.$)$

Part $4$

b$.$ The results from the last $5$ samples of $7$ packets are shown below. Is the process in$$ control? Explain.

$$

Sample

x overbar

R

$1$

$42$

$3$

$2$

$42$

$6$

$3$

$43$

$9$

$4$

$44$

$4$

$5$

$42$

$5$

The process variability is

in

statistical control and the process average is

out of

statistical control.$$ Therefore, the entire process is

in

control.