Quality Quiz from Professor Cleary
Congratulations:
"Yes" is the correct answer!
Click here for a more complete video explanation.
YES. Awana is worth her weight. She's right about
the chart's validity.
The chart did not take into account the fact that
the number inspected varied from a low of 392 on February 17 to
a high of 2306 on February 10. As you will recall, the calculations
for pchart control limits are:
When using a pchart, these formulas apply as long
as the sample size varies no more than 25 percent of the average
sample size ().
In this case, SQCpack shows the average sample size of
1192.32. If the sample size varies by more than 25 percent, an adjustment
must be made to the control limits. In cases where the sample size
is larger than 25 percent of the average sample, the control limits
are adjusted so they will be tighter. This may seem intuitive, since
the larger sample size would indicate a higher confidence in the
estimate of p.
This adjustment can be seen on sample #16, taken on February 10, where the sample size is 2,306, almost twice the size of the average sample size of 1,194. The chart above indicates that this point is out of control, and an adjustment to the control limits suggests an assignable cause.
On the other hand, sample #21 (February 17) indicates
that the point is in control, although on the first chart it appeared
clearly above the upper control limit. But an adjustment to the
control limits is necessary to analyze this point properly, since
sample sizes are different. In this case, the sample size is 392,
substantially less than 25 percent of the average size (1,194.32).
SQCpack has properly adjusted control limits to reflect
the small sample size. One might expect the control limits to become
larger, since a smaller sample has less information and this leads
to a wider margin for error.
Allie seems to have steered down the
wrong alley, but she has walked us through p charts and made the
observations that when samples vary by more than 25 percent of the
average sample size, an adjustment in the control limits must take
place.
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