July 2002

Vol. 4, No. 7

Quality Quiz

Quality manager Hugh N. Kry is in deep trouble. His boss, Cal S.Terol, has been ranting for days about the diminishing quality of the company's products. The firm, which manufactures a variety of toy products, has undergone scrutiny by a major consumer journal; in addition, stores are complaining about high rates of return for the toys that Play With Us, Inc., manufactures.
Cal S. Terol orders Hugh to hire 'as many inspectors as we need ' to keep defective products from going off the assembly line and being shipped to stores. Hugh, who rarely responds to his boss in anything but a meek 'Yes, sir, ' summons the courage to point out that a system of prevention is always preferable to one of detection. 'I hired you to prevent mistakes, ' the boss shouts. 'And that hasn't worked, so we'll inspect every blasted toy that we make, ' ordering Hugh to hire ten inspectors immediately, at minimum wage. (The local fast food store, it should be noted, is currently paying $9.50 per hour and still has a 'Help Wanted ' sign in its window.)
Knowing that he must find inspectors immediately, Hugh goes to the local unemployment office and pleads with people in line, finally attracting ten who say they will show up on Monday.
Although only eight workers actually appear on schedule, Hugh is undaunted, and decides to teach them about X-bar and R charts on the first day. The training room is set, with calculators at each station, and he begins to lecture. These new students do well with the range:
                        X highest X lowest
They have a hard time calculating averages, however, in spite of Hugh's use of batting averages as a model for the calculations. They seem to be totally puzzled by the statistical symbols:
He suddenly recalls the use of median charts, where only the median is recorded, rather than the mean, popularized by Dr. Clifford after World War II. Common practice called for sample sizes of 3 or 5, so no math was necessary. For example:
Data:                14, 12, 17, 19, 15
Median:            12, 14, 15, 17, 19
To calculate the median, the data must be ordered from the smallest to the largest number; the middle number is the median. In this example, this would be 15.
Range:              19 12 = 5
Excited by this approach, Hugh teaches his motley crew how to do median charts. Unfortunately for him, one of the new hirees had been employed previously as an inspector. Just as Hugh finished his brilliant lesson, this inspector asked why the A 2 factor is different for median charts than for X-bar and R charts. He had used his calculator to figure that the A 2 factor for median charts, called A 2 tilde (~) is about 25 percent larger than the A 2 for X-bar and R charts.
Hugh, flushed from his spectacular performance in teaching median charts, now found himself at a loss. Not wanting to embarrass himself by admitting that he did not know, he pointed out that the square root of .0625 is equal to .25. The old inspector, amazingly, accepted his answer since he himself was not adept at math. Was Hugh N. Kry's response appropriate?
A. Yes
B. No


Copyright 2002 PQ Systems.

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