# how to canculate the process sigma level

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• #39105

Ruddy
Participant

Hi there,
Now the six sigma is buzzword in many area. My question is how to calculate process sigma level.
For exmaple, suppose there is no shift in process, our process means is 100, taget is also 100,process sigma(by R/d2 calculating) is 1.8, specification is 90–110,  Question1: how to calculate sigma level?  is it (110-90)/6*1.8? Question2: now I am also confusing how to calculate the cpk of this ?
thanks

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#118219

Shri
Member

What’s the standard deviation of your process?

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#118220

Thai
Participant

Michael,
The process Sigma can be calculated by 3xCp where the Cp is
(USL-LSL)/(6*Standard Deviation)
The Cpk is the minimum value of:
(USL-Mean)/3*stdev or (Mean-LSL)/3*stdev
Kirk
By the way, there is disagreement among peoples as to how to calculate Sigma level from Cp or Cpk.  Some people say you multiply 3*Cp others say 3*Cpk.  Since your process is centered, Cp will be close to Cpk so it doesn’t make any difference.

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#118221

Shri
Member

So, as I said, you need the SD to find out the capability of your process. So, the Q is what’s your Std. Deviation?

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#118222

Thai
Participant

I would assume that since Michael stated his Process Sigma is 1.8 (however he calculated it, he said R/d2 which may be Rbar/d2 or the Moving Range method) so therefore the Process Standard deviation is 1.8.
Kirk

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#118224

Anonymous
Participant

If your specification is 90-110 then you can take the total number of units produced either within or outside of those specs in order to determine how many units (out of all units produced) are within that the specification.
For example, if 500 are produced and 484 are within the specification and 16 are either less than 90 or greater than 110, then you can assume that your accuracy percentage is 96.4% (or .964).
The easiest way to calculate process sigma  is to use the following formula in excel:
normsinv(.964)+1.5
The result of the first part of the equation will be your process sigma level.  Also, you always add 1.5 to account for the shift.

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#118225

Anonymous
Participant

I meant to write that the formula will give you the process sigma level.  Not that the first part of the formula will give you process sigma.

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#118228

Mikel
Member

There is no disagreement. those that think its 3*Cpk are just wrong.

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#118230

Utah123
Member

Stan,
Could you elaborate?  Also, how is an argument made for Z value over Cp/Cpk (as GE and others favor Z relative to Cp/Cpk) for describing process capability if you simply multiply by a factor of three?  Then it is simply a matter of conversion and is a moot point….what am I missing?

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#118231

Mr IAM
Participant

Stan,
Why is Cpk*3 just wrong?  If that is wrong, Cp*3 cannont certianly be correct either as they are equal if the process is centered.   Is it in the cases of where you have a double sided tolerance rather then single?  Does Cpk take into account both “tails” that are beyond the specification limits?  I’m interested in your logic, not in an arguement.
Thanks, Mr IAM

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#118234

Neeraj
Participant

Mike,
I think the first way of calculation that you have mentioned is primarily used to calculate the process capability ie Cp wherein the tolerance of the process ie (USL-LSL) is checked against the process deviation…………….as far as the process sigma level is concerned that could be done with the excel function too……….
Kindly correct me if Iam wrong……………….
Rgds/*-

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#118236

Thai
Participant

Stan,
No argument here.  I also must say that I have never found much use for a Sigma value (other than to initiate some interesting and enjoyable debates among certain Six Sigma professionals).  The only time I have reported a sigma value is in a Six Sigma project report to management many years ago…
Kirk

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#118244

Mikel
Member

Go read the original material from Motorola. They had a two page “What is Six Sigma” which defined a two sided spec that, when centered, was +/- 6 standard deviations from either spec. There is a picture showing a normal curve  in solid black with two more curves in dashed lines, one shifted -1.5 and one shifted +1.5. This is the official definition, like it or not. An assumption of centered and measuring distance from this assumption. There is also an assumption of a reasonably controlled process not moving more than +/- 1.5. This was empirically derived and there is no theoretical derivation no matter how many people make such stupid claims.
Is the assumption of two sided always valid – of course not. Is the assumption of centered being the desirable target always valid – of course not. Are the assumptions the most common scenario we encounter? Yes.
On valid cases of a one sided spec, it is 3*Cpk. But just remember that all of the assumptions of normality and independence of mean and standard deviation just went out the window as well.
Cpm is the better metric anyway. All this crxx of zlt, zst, zbench are just inventions of Dr. Harry that were never needed in the first place.
All you really need is an understanding of margin vs customer expectations in the absense and presence of factors which can cause both mean and standard deviation to change. This could be done with a rational data collection scheme and histograms.

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#118260

AndyU
Participant

Stan,
If tolerances are based on individuals and targets are based on averages, I know where I would prefer to have a reference!
Cheers,
Andy

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#118282

Mr IAM
Participant

Stan –
Thanks for your explanation.  I agree with your thoughts.  The problem is that we have many people teaching it many different ways.  I for instance have a BB Primer that defines Sigma as Cp*3 (reference Indiana Quality Council CSSBB Primer).
My understanding is the value of reporting sigma Zst or Zbench Within, is so we have people using one metric.  Rather then some people using %, some using PPM, some using DPMO, some using DPU, some using CP, some using CPK etc God the list of metrics is endless.
Thanks, Mr IAM

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#118284

Whitehurst
Participant

Hi Stan the same old story about Cpk Ppk Cp we were having few days back I think you got this time right Zst = 3 Cp or 3CPk but the assumptions donot hold good in this case.
Take care

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#119025

Slavik
Member

Thanks

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#119158

Anshul
Participant

Hi Kirk,
You use Cpk only in case of non centered processes. Other wise Cp should be equal to Cpk.
Well I will like to know about a case whr Cpk is not equal to Cp in a centered process
Regards
Anshul

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#174055

ehaque
Participant

Hi there,
I know Sigma Level = 3*Cpk+1.5
in the above equation why we are multiplying cpk by 3, why 3?
Thanks
ehaque

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#174057

Participant

Well you don’t have it exactly right, but I will explain about your question.
The CpK is a calculation which divides the distance between the mean of the process and the nearest specification limit by 3 standard deviations. So if you have a CpK of 2 and multiply it by 3, you would have 6 sigma capability.

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#174069

Ron
Member

Two ways to go for calculating process sigma (this is not standard deviation)
Yield = (1-DPO) X 100 where DPO means defects opportunities…look up sigma on a table (you can download from internet)
Alternate (preferred)
Using Excel  – NORMSINV((1-DPMO)/1,000,000) + 1.5
Where DPMO is defects per million opportunites

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#174117

Participant

Check out any website referring to Fred Spiring. He was teaching somewhere in Canada the last time I talked to him. His seminal article co-authored by Chan and Cheng is in The Journal of Quality Technology, vol 20 (1988), page 162.

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#174118

ehaque
Participant

Hi,
Sigma level = 3*Cpk+1.5
My question is why we multiply Cpk by 3 in the above equation? why 3?
Cpk = min{ (usl-mean)/3s, (Mean-lsl)/3s}
why we are taking minimum in the above equation?

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#174119

Almudena
Participant

Let’s review definintions:
Six Sigma Level = Min{(USL – y)/s, (LSL-y)/s}
Cpk = Min{(USL – y)/3s, (LSL-y)/3s}
Therefore Six Sigma Level = 3*Cpk
Another term is Six Sigma Capability = Sigma Level + 1.5
e.g. If Cpk = 1.5, then Sigma Level = 4.5, Sigma Capability = 6.0 and DPMO = 3.4
I hope it helps.
Almudena

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#174120

ehaque
Participant

Thanks almudena,
Sigma level = 3*Cpk
i like to know the explanation/logic why 3 in the above equation?
Thanks
ehaque
Let’s review definintions:
Six Sigma Level = Min{(USL – y)/s, (LSL-y)/s}
Cpk = Min{(USL – y)/3s, (LSL-y)/3s}
Therefore Six Sigma Level = 3*Cpk
Another term is Six Sigma Capability = Sigma Level + 1.5
e.g. If Cpk = 1.5, then Sigma Level = 4.5, Sigma Capability = 6.0 and DPMO = 3.4
I hope it helps.
Almudena

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