Problem $1$:

As a quality inspector at GE$,$ your primary job is to monitor the average life of a line of lamp bulbs. The

following sample data on bulb life $($in $1000$ hours$)$ were collected when the production process was

known to be in control. Each sample consisted of $6$ items:

a$.$ Calculate the $3$ upper and lower control limits and the center lines for the mean $($X$-$bar$)$ and range $($R

charts. Use the "factors" given in class slides.

b$.$ Recently, GE changed their supplier of a key component. To evaluate if this change has an impact on

bulb life, the following $10$ samples were collected after this change.

$1.)$ Using the upper and lower control limits and center lines you computed in part $($a$),$ plot the sample

mean and sample range for each of the $10$ samples on the appropriate control chart.

$2.)$ Is the production process still in control? Why or why not?