You run a blood testing lab at a large urban hospital. Turn around time for tests is a critical quality characteristic. Lately you have become concerned that the variability in turn around times from test to test has increased a lot. You are not hearing a lot of complaints from your internal customers, but the complaints that you do receive are about turnaround times that are wildly different from historical averages. In other words, some waits are have gotten really really long even if the average wait has not changed. On the other hand, you've received positive comments from other internal customers thanking you for getting them their test results in much less time than normal.

Luckily, your team has been tracking turnaround times using statistical process control. The number in the body of the table is the turnaround time in hours for the most common kind of test. Your lab operates round the clock. You remember from SCM$301$ that you should always use an x bar and r chart together. Which chart is likely to reveal the problem described here?

Sample Test $1$ Test $2$ Test $3$ Ave $($x bar$)$ Range $($r$)$

$191011$

$211812$

$38814$

$412145$

Compute the average or each sample $($x bar$)$ and the range of each sample $($r$)$ to validate yourself or to help you figure out the answer.$--$i$.$e$.$ is it the average or the range that suggests something in the process is changing over time?

Group of answer choices

The averages of the samples $($x bar$)$ are very stable; however the range is growing drastically. An R chart would likely show that the process is going "out of control"

The variation $($r$)$ within each sample is very stable; however the sample averages $($X bars$)$ are growing drastically. An X bar chart would likely show that the process is going "out of control" s

X bar bar $($the center line on chart if we were to make one$)$ is stable. So an X bar chart would suggest to us that the process has gone "out of control"

The average of the ranges $($R bar$)($the center line on chart if we were to make one$)$ is stable. This suggests the process has gone out of control.