Vol. 7, No. 04
from Professor Cleary
Marty is not alone in this misunderstanding of Cpk and its meaning. One way of approaching Cpk is with an understanding of what a Cpk of 1.0 means. Assume a process as below:
The Z upper and Z lower values are both 3, so Cpk is equal to 1. To see this more clearly, observe that the USL is 3 values, or 3 standard deviations, to the right, and the lower spec limit is three values, or 3 standard deviations, to the left. This provides an explanation of the fact that with a Cpk of 1, at least 99.73 percent good parts are produced.
Why 99.73? Because in normal distribution, plus 3 standard deviations and minus 3 standard deviations captures 99.73 percent of the area under the curve.
Why "at least"?
Consider this example:
As this indicates, the Cpk is again 1, because the was 3. The fact that was 5 is irrelevant--the process would no doubt be producing more than 99.73 percent good parts.
Essentially the Cpk is a more conservative index than Cp.
Out of the game but undaunted, Marty has purchased CHARTrunner software and is discovering the new worlds of Pp and Ppk. Let's see next month how he handles these new capability indices.
Copyright 2005 PQ Systems.
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