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Quality Quiz:Professor Cleary
Another quiz from Professor Cleary

Cora D’Appel is puzzled. Cora and her friend, Deleta Messtake operate a plastics extrusion plant near the woods. The company, Eden Decor, makes decorative items with a garden theme. Some of these are clear plastic terrariums, molded resin ducks, and artificial decorations for bird baths. Customers of the company founded and owned by Hugh G. Ego are primarily retailers from the Midwest and large landscape companies who buy products for their customers.

Since Hugh is keenly interested in high quality, he wants to use SPC charts to assure the uniform dimensions of the extruded products. Cora is excited to follow along with this quality initiative, but Deleta doesn’t pay much attention to this process, since she believes each product should be unique. Nonetheless, she helps her friend gather data relating to the dimension of plastic rods that are used to hang mobiles, one of the company’s most popular products.

Cora, as noted, is puzzled. A technician has been keeping data and creating X-bar and R charts to analyze the rods’ dimension. The sample size used is 5, but from time to time the sample size is slightly smaller. Cora is trying to determine why control limits change on the chart when the sample size is smaller, becoming wider as sample size drops.

Deleta insists that none of this matters. “At least we check them,” she points out, and since end users rarely purchase more than one of the rods, they will have no basis for comparison of the dimension on like products, she reasons. This is not good enough for Cora. The question keeps her awake at night and focuses her attention much of the time.

“I’ve got it!” she shouts one night as she’s letting the cat out. “If a sample size is smaller, there will be less variability in it than if it were a larger sample!” Ignoring the cat’s pleas to come back into the house, Cora races to the plant to test her theory.

Will her theory be correct? Will her cat forgive her for leaving him out for the night? Will Deleta care? Let’s settle the statistical issue first.

a) Yes, Cora has hit on something that explains the wider control limits.

b) No. She should let the cat in and ponder some more.


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