Vol. 7, No. 07
from Professor Cleary
Maura has this statistical concept confused with a popular steak sauce, to be sure, but the analogy breaks down even without its semantic confusion.
Control charts were introduced in the 1930s after statistician Walter Shewhart and his colleagues at Bell Labs made them known, identifying their purpose as one of monitoring processes by sampling, calculating averages, and plotting those averages on charts. They developed control limits by using the process average (average of the averages, or ), moving three standard errors above this process average to create the upper control limit, and three standard errors below the process average, to what is known as the lower control limit.
Shewhart’s classic text, Economic Control of Quality of Manufacturered Product ( New York: D. Van Nostrand Co., 1931), provides an example of tensile strength of steel, demonstrating how to calculate upper and lower control limits.
Because of the technology limits of the time, the calculation was complex and fraught with barriers. To find the square root of a number, one needed to use a slide rule or rely on finding a table of square roots in a textbook. Calculation of the standard deviation, expressed in the following formula, represented a great deal of arithmetic under the radical sign, in addition to the complexity of computing the square root.
As an alternative to this complex calculation, Shewhart developed an estimate . This was accomplished by developing what is known as . Realizing that it was easier to estimate variability with than standard deviation. , when multiplied by , provides a sound estimate of .
Far from rendering the calculation complex, actually makes it easier. Sort of like using bottled steak sauce rather than making your own.
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