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Calculated error

In Expert Answers (April 2011), Jeffrey Vaks writes a great column—with one minor exception. His example uses a mean of 95 and a standard deviation of 1 against a specification limit of 100-90, resulting in a Cp of 1.67 and a Cpk of .83.

He then proceeds to show that if the specification limits are expanded to 103.5-86.5, the new Cpk would equal 2.0, which is larger than the original Cp of 1.67. The only problem is that the new specification limits call for a new calculation of Cp:

which gives a result of 2.83 and thus is still larger than his calculated Cpk of 2.

The simple fact is that Cp is the limit of Cpk—always was, always will be. He also goes on to say there is a similar effect when the standard deviation is reduced. That also requires recalculating the Cp, as well as the Cpk.

John C. Finley
Carmel, IN

Author response: The reader’s comment is correct that with changes in specifications and process variation, Cp and Cpk both need to be recalculated. The question was how Cpk can be larger than Cp. This is what I explained: It only can be larger than the original Cp after the specification is expanded or the process variation is reduced.

Indeed, I neglected to mention that the new process has a new Cp that cannot be exceeded by the new Cpk, though the new Cpk exceeds the original Cp.

Jeffrey E. Vaks
Roche Molecular Diagnostics
Pleasanton, CA

Truth of the matter

Dean L. Gano has written a great article on a very deep topic ("Are You a Good Problem Solver?" May 2011) . But I find the following statement a bit controversial:

"People’s understanding of reality is as unique as everyone’s fingerprints, formed from every experience of their lives by a nervous system with limited and varied senses, and a brain that provides for an infinite set of perceptions using an endless set of strategies to establish their own truth."

It is OK up until the last four words—"establish their own truth." I think what the author is trying to convey is that we all have varying perceptions or interpretations of "absolute truth," depending on our own unique background of experiences among other things. This seems to suggest that truth is a moving target. This is not the case.

It’s a subtle but very important distinction that should not be lost or misconstrued. If there were no absolute truth, how can there be any science or fact? Everything would be relative and subject to infinite variance, or at least as much variance as there are humans on Earth.

Jay Edwardson
San Clemente, CA


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