# process capability

Six Sigma – iSixSigma Forums Old Forums General process capability

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• #29405

Michele
Participant

What process capability level does the 6 sigma program try to achieve (optimally)?

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#75281

Cordoba
Participant

Cpk =1.67  means 6 sigma level=3.4 PPM
Regards

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#75282

Cravens
Participant

CpK is the smaller of (USL-Xbar)/3 sigma or (LSL- Xbar)/3 sigma.  More simply:  (Closest spec limit – Xbar)/3 sigma is the calculation for CpK.  In any case, the distance from the closest spec linit to the process mean is divided by 3 sigma.  Therefore, if this smallest distance has 6 standard deviations divided by 3, then a 6 sigma process is equal to 6/3, or a CpK of 2.00.  A CpK of 1.67 is 5/3=1.67.  This is a 5 sigma process, not a 6 sigma process.

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#75284

Gabriel
Participant

I am not an expert in SS at all, but from what I could get (mainly from this forum) I understand that 6 sigma level assumes a process shift (in the long term) of 1.5 sigma from the target (center of spec.). This fact of the process shift was largely discussed in previous threads, and I won’t add nothing about it.
But what I can say is that:
– The name “six sigma” comes from assuming that the process variation contained within the average value +/- 6S is fully within specification. At least, this is Cp=2 and Cpk=2. This leads to much less than 3.4 PPM (I dont remember now but think it was less that 1 part per BILLON)
– Then, somehow we get to the 1.5 sigma shift. So we have Cp=2 (like before) but now Cpk=1.67. This leads to the famous 3.4 PPM. I am not saying that I agree with the 1.5 sigma shift, but this is how it is axplained that a process with a Cpk=1.67 (average 4.5 sigma away from the closest limit) is said to be a 6S process (still, because Cp=2, the width of the spec is equal to the width of the process +/-6S, but shifted).
– Cpk=1.67 is not equal to 3.4 PPM, unless you have a Cp=2. So it is not correct (or not complete) to say, as in the forst response, that 6 sigma is Cpk=1.67 and that this is 3.4 PPM. In fact, a process with a Cpk=1.67 and a Cp=1.67 will double the PPM to 6.8, and will not be considered a 6S process. The spec limits would be cincident to the process average +/- 5S.

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#75285

Ashok Sarkar
Participant

This has reference to so many discusssion on SIx Sigma. We may conclude in the following way;
1. If Cpk=1.5 and Cp=2 ( Shift of average is 1.5 sigma) then ppm is 3.4 and this will be true for one side specification (offcouse Cp is not applicable). This is we understand as six sigma level and this means at worst case process will deliver 3.4 ppm defective product (May be we use the word opportunity also).
2. If shift is more or less than 1.5 sigma then the ppm level changes.
Regards

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#75294

Gabriel
Participant

My previous post is full of mistakes and if I could I would delete it. It seems that my brain was on strike yesterday. Forget (and forgive)everything I said about 5 sigma and Cpk=1.67
Six sigma level is taken as 3.4 PPM what, for a normal distribuited process, is equivalent to Cpk=1.5 and Cp=2. This a process where its +/-6S distribution width is equal to the spec width, but the process average is shifted 1.5S from the center of the spec (i.e the process average is 4.5S from the closer spec limit and 7.5S form the other limit). Note that Cpk=1.5 alone is not enough to get this 3.4 PPM. With Cp=Cpk=1.5 you double this value to 6.8 PPM.

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#75297

RR Kunes
Member

Cpk =2.0

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#75320

TCJ
Member

The goal of the “6 sigma program” is to eliminate defects (0 defects).  Is that practical?  Of course not; therefore, we strive for incremental improvement i.e. take a 2-sigma process to 3- sigma, 4 to 5, etc.  The definition of a 6 sigma process as mentioned earlier (Cp=2, Cpk = 1.5).  The process potential Cp is 2 defects per billion and the capability with the inclusion of the1.5 sigma shift, Cpk = 1.5, is 3.4 defects per million.

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