Dramatic Statistics, Tragic Flaw

Hubris stalks Simsack as he demonstrates the simplicity of process capability.

One of Greer Grate & Gate’s customers, Mandible Manacle Manufacturing, makes handcuffs and sells them to law enforcement agencies throughout the United States and Singapore. After an unfortunate spate of separations and failures in cuffs used to restrain criminals, MMM has insisted on higher quality throughout its manufacturing processes and has demanded that Greer Grate & Gate’s components be produced with a CpK of at least 1.

For Hartford Simsack, this is a piece of cake. In fact, he sees this as an opportunity to instruct--and hopefully impress--his assistant, Aiden Abett. He begins by writing formulas on a whiteboard.

The data comprise 14 samples, with sample sizes of two:

His calculations look like this:

In this case:

To calculate the CpK, Simsack explains that one should divide the smaller Z value by three:

Simsack has no doubt impressed Abett, although the student’s eyes have glazed over slightly. “That’s all there is to it,” Simsack concludes.

A week later, Abett brings Simsack a printout of the same data, with the X-bar and R charts as well as the histogram that he’s created from the data. Puzzled, he asks Simsack to explain the points that seem out of specification. Simsack dismisses the printout as a computer error because “Everyone knows that a CpK of 1 or more shows that you’re making virtually all good parts.”

Is Simsack correct in his observation?

Simsack is, of course, incorrect--again.

Arrogant enough to dismiss any obligation to check his conclusions, Simsack failed to check the two critical assumptions that are vital to capability studies:

The X-bar and R chart must indicate that the process is in control.

Data must conform to a normal distribution.

As the charts below indicate, Simsack’s data violate not one but both assumptions. Unfortunately, this means his conclusion--that a CpK of 1.17 represents a great accomplishment--is tragically flawed, especially when the printout shows 21.4 percent of the data are out of specifications.

About the author

Michael J. Cleary, Ph.D., founder and president of PQ Systems Inc., is a professor emeritus of management science at Wright State University in Dayton, Ohio.