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Departments: SPC Guide

Photo: Michael J. Cleary, Ph.D.

  
   

Five Easy Samples
A magic number simplifies analysis.

Michael J. Cleary, Ph.D.
mcleary@qualitydigest.com

 


Dr. Tad E. Gotistic is confident of his ability to instruct the emergency room nursing staff at St. Recover in the Long Run Hospital in the fundamentals of statistical process control, despite the fact that he understands how to use X-bar and R charts but little else in the way of statistical applications. However, he assumes that the staff doesn't know as much as he does, and that gives him an advantage. At least, that has always been the case whenever he's had to prove his knowledge in a variety of areas.

During the seminar in which Gotistic learned about charting, the instructor provided an example using 15 samples of five each, and Gotistic employs the same example when instructing the nursing staff. Illustrated below is the chart he uses in the class.

Gotistic created X-bar and R charts and was deeply involved in deriving control charts when one of the nurses asked why he'd selected a sample size of five. "Why not six or seven or even 10?" This nurse had, in fact, also participated in a seminar that offered an overview of SPC, and the instructor had used a sample size of five in that instance as well.

Gotistic had a ready answer, asserting that selecting a sample size of five was required for statistical precision, obliquely suggesting that any other sample size would be flawed in its statistical calculations. "Trust me," he said, "This is statistically sound."

Why is using a sample size of five conventional practice?

a. It's grounded in statistical accuracy, as Gotistic asserts.

b. Using a sample size of five is the most economical choice.

c. A sample size of five renders the arithmetical calculations more convenient.

d. A sample size of at least five creates validity, but there's no magic in the number itself.


Answer c is correct. A sample size of five allows for a shortcut to calculate the average. Five is the conventional sample size not because of its link to any statistical principle, but because it makes calculations more convenient.

By taking the sum of the samples, multiplying by two and moving the decimal point one place to the left, the same result ensues, as illustrated:

Moving the decimal one place to the left generates 12.4.

Remember that the control chart was developed during the 1930s, long before affordable calculators or PCs were available for statistical calculations.

By the way, don't confuse your grade-school kids by introducing them to this "new" way of calculating averages. This method works only if the sample size is five.

About the author

Michael J. Cleary, Ph.D., founder and president of PQ Systems Inc., is a noted authority in the field of quality management and a professor emeritus of management science at Wright State University in Dayton, Ohio. A 29-year professorship in management science has enabled Cleary to conduct extensive research and garner valuable experience in expanding quality management methods. He has published articles on quality management and statistical process control in a variety of academic and professional journals. Letters to the editor regarding this column can be sent to letters@qualitydigest.com.