Quality Quiz from Professor Cleary

Congratulations:
"Yes" is the correct answer!

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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 p-chart control limits are:

When using a p-chart, 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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