Vol. 7, No. 02
from Professor Cleary
Marty should have read pages 249-252 of Practical Tools for Continuous Improvement (Graham and Cleary), which shows a step-by-step process beginning with a clear visual of the situation:
The book then explains how to calculate the percentage of parts above the upper spec limit of 14. Remember, we have assumed that this is a normal distribution, so it is important to see how many standard deviations the upper spec limit is from the center (10.00) of the distribution.
Another way of stating this is to determine how many values the upper spec limit is from the mean, following this formula:
This means that the upper spec limit in this case is two standard deviations to the right of the mean.
You may recall the standard normal distribution table, from your college stat course. The table is used to determine the area under the normal curve. (You may choose to listen to the video, for further understanding.)
The first column in this table is labeled and represents the number of standard deviations. The column to the right indicates the area to the right of the value that is under the normal curve.
In this case, is equal to 2.00, and the column to the right is .0228, indicating that by going two values to the right, the area under the curve is .0228, or 2.28 percent. In the example, then, 2.28 percent falls outside the upper spec limits.
Next, look at the left side to see how many values the lower spec limit is below the lower spec limit.
Referring again to the standardized normal distribution table, it is clear that the largest value for is 4.0. This means that there is virtually no area under the normal curve to the left of equal to 5.
Finally, to calculate the total percent outside of specifications for this example, it would be
2.28 + 0 = 2.28%.
This all may seem to be a great deal of trouble, but it is important to understand what your CHARTrunner or SQCpack means when it ways "out of spec total = 2.28%."
Next month we will calculate the Cpk.
Click here for a .pdf file of relevant sections of Practical Tools for Continuous Improvement.
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