RE: Interpretation of Cpk

[Steven_S_Prevette@rl.gov]

A Cpk of 8 is certainly possible.  All Cpk is is a ratio between the control
chart control limits, and the specification of the customer.  Literally, you
take the distance between the customers specification, and divide it by the
distance between the control chart 3 standard deviation control limits.

One could convert Cpk to parts per million, but you have to make a few
assumptions.  Most people look up the equivalent Cpk to ppm by going to the
Normal distribution.  This is not necessarily a good assumption.
Tchebychev's inequality would also work.  A Cpk of 8 is equivalent to asking
- what is the probability of exceeding 8*3 = 24 standard deviations from the
average in either direction?  Tchebychev would give the result of 1 minus 1
divided by 24 squared.

The six sigma people discovered that a Cpk of 2.0 was a good place to
operate at.  But they have added confusion to the Cpk issue by subtracting
1.5 sigma off of any conversion of Cpk to parts per million.

Dr. Deming would caution us against this sort of use of data.  This crosses
into the area of "levels of significance" and "hypothesis testing".  Also,
the Cpk limit is based upon 'brick wall' limits, rather than a loss function
such as Taguchi.  There is a good paper on the Deming List home page by Bill
Latzko at 
    http://deming.ces.clemson.edu/pub/den/six_sig.pdf which discusses
six sigma and the Cpk issue.

Steve Prevette
QA Engineer, ESH Radiological Compliance
Fluor Hanford, A Fluor Global Services Company
ASQ Certified Quality Engineer
steven_s_prevette@rl.gov
509-373-9371