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  Statistical Techniques and 6 Sigma
  Calculating Defect Rate from a Cpk value

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Author Topic:   Calculating Defect Rate from a Cpk value
Jim Bongard
posted 13 January 2001 09:55 PM           Edit/Delete Message   Reply w/Quote
Is there a simple formula for determining a defect rate (Defective Parts Per Million) for a given Cpk value?

Thanks in advance.

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Lurker (<10 Posts)

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From:Melbourne Australia
Registered: Jan 2001

posted 15 January 2001 10:15 PM     Click Here to See the Profile for thebigbear   Click Here to Email thebigbear     Edit/Delete Message   Reply w/Quote
Hi Jim,
In my search for info on a similar topic (which I posted a request on this site) I've came acrosss an article that may help you. I can't recall the exact title but I
have the referance for you.

Quality Engineering Journal, Vol 9, No2, Dec 1996, pages 305-316.

It discusses the affects of the various types of ditributions on Cpk and the affects on DPPM. It also notes that Skewness and Kurtosis has a significant impact on DPPM.

Hope this helps and hope the details are correct.

Best of Luck
Nick Viney

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Marcel Boere
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posted 17 January 2001 03:34 PM     Click Here to See the Profile for Marcel Boere   Click Here to Email Marcel Boere     Edit/Delete Message   Reply w/Quote
Its easy:

Cpk is commonly used as a process capability measure for normally distributed populations.
The Cpk value is directly related to both the Sigma and the 'distance'of the pop.average to the closest specification limit.
Thus Cpk=1 --> average 3 sigma from limit. Cpk=1.33 --> average 4 Sigma, andsoforth.
In every statistical study book you can find the normal distribution table. Look, in the one side table, for the z(?) value (z in this case equals the number of sigma's you found earlier above). In the table you will find the applicable percentage (or ppm) of the population outside the closest specification limit.

Please note you can only use the one sided table if Cpk<< Cp. Other wise repeat the procedure for each limit (upper and lower).

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