Vol. 11, No. 6
June 2009
PQ Systems
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Quality Quiz from Professor Cleary
Fishing for answers

LaMal d’Mer is puzzled. LaMal and her sister Aqua d’Mer own and operate a plastics extrusion plant near the sea. The company, Synk R Swym, makes decorative items with an ocean theme. Some of these are clear plastic bubbles, molded plastic shells, and fish ornaments. Customers of the company, founded by their father Neptune d’Mer, are primarily retailers from the Midwest and large cruise ship companies who buy products for their passengers.

Since LaMal is keenly interested in high quality, she uses SPC charts to assure the uniform dimensions of her extruded products. Aqua doesn’t pay much attention to this process, since she believes each product should be unique. Nonetheless, she helps her sister gather data relating to the dimension of plastic rods that are used to hang fish decorations, one of the company’s most popular products.

LaMal, 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. LaMal is trying to determine why control limits change on the chart when the sample size is smaller, becoming wider as sample size drops.

Aqua 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 LaMal. 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, LaMal 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 Aqua care? Let’s settle the statistical issue first.

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

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


Click here for a more complete video explanation

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