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How to calculate the sigma level of a process and Relationship of DPMO
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 90110,
Question1: how to calculate sigma level?
is it (11090)/6*1.8?
Question2: now I am also confusing how to calculate the cpk of this ?
thanks
michael

24th April 2005, 01:14 PM

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Calculating sis sigma
The calculation of a Sigma level, is based on the number of defects per million opportunities (DPMO).
In order to calculate the DPMO, three distinct pieces of information are required:
a) the number of units produced
b) the number of defect opportunities per unit
c) the number of defects
The actual formula is:
DPMO = (Number of Defects X 1,000,000)
((Number of Defect Opportunities/Unit) x Number of Units)
Example:
A manufacturer of computer hard drives wants to measure their Six Sigma level.
Over a given period of time, the manufacturer creates 83,934 hard drives.
The manufacturer performs 8 individual checks to test quality of the drives.
During testing 3,432 are rejected.
Defects 3432 DPMO 5111.158768
Opportunities 83934 Sigma Level 4.1
Defect Opportunities per unit 8
Six Sigma Table: 1 690,000
2 308,000
3 66,800
4 6,210
5 320
6 3.4
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25th April 2005, 12:42 AM


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Thanks for the help on this one, Bob!
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27th April 2005, 11:57 AM


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Quote:
In Reply to Parent Post by Bob Ablondi
The calculation of a Sigma level, is based on the number of defects per million opportunities (DPMO).
In order to calculate the DPMO, three distinct pieces of information are required:
a) the number of units produced
b) the number of defect opportunities per unit
c) the number of defects
The actual formula is:
DPMO = (Number of Defects X 1,000,000)
((Number of Defect Opportunities/Unit) x Number of Units)
Example:
A manufacturer of computer hard drives wants to measure their Six Sigma level.
Over a given period of time, the manufacturer creates 83,934 hard drives.
The manufacturer performs 8 individual checks to test quality of the drives.
During testing 3,432 are rejected.
Defects 3432 DPMO 5111.158768
Opportunities 83934 Sigma Level 4.1
Defect Opportunities per unit 8
Six Sigma Table: 1 690,000
2 308,000
3 66,800
4 6,210
5 320
6 3.4

Dear Bob,
thank you so much for your infomation. I have anther way to calcuate it, but the result is different. Would you please give me some suggestion?
DPU: 3432/83934=0.0408
Y=FPY=e(DPU)=e(0.0408)=0.96
probability of a defect {P(d)}=1Y=10.96=0.04
using Z value table is 1.75 sigma
so it is different.
thanks
Michael

27th April 2005, 05:04 PM

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Quote:
In Reply to Parent Post by jackylpt
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 90110,
Question1: how to calculate sigma level?
is it (11090)/6*1.8?
Question2: now I am also confusing how to calculate the cpk of this ?
thanks
michael

The method shown is with a plus/minus 1.5sigma shift based on Motorola's allowance for process variation in manufacturing.
Bob
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27th April 2005, 05:28 PM


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That pesky 1.5 sigma shift sure makes life difficult! And the question of what an "opportunity" is!
There is a "Sigma calculator" you can use at
http://www.isixsigma.com/sixsigma/si...asp?m=advanced
If you have a situation with...
* 83934 units
* 3432 defective units
* each unit is 1 opportunity
Then you have 4.1% defective = 41,000 DPMO. The calculator above says that if the process is centered then this is a 1.74 sigma process. Using the "standard" 1.5 sigma shift says this is a 3.24 sigma process. (these numbers aren't too hard to come up with  they assume a normal distribution that would produce a similar number of defects at the closer spec limit.)
If you considered each test as an opportunity, then you would have 8 times as many opportunities, and a correspondingly better sigma value.
For the example you gave, with xbar=100, limits at 90 & 100, and sigma = 1.8, you are currently (110100)/1.8 = 5.56 sigma from the closest spec limit. However, since the "standard" calculation assumes that the process might drift 1.5 sigma, i.e the center might drift by 1.8*1.5 = 2.7. You would then be only (110  102.7)/1.8 = 4.06 sigma from the closer spec limit. This would, I believe, be the "official" sigma level for the process.
Tim F
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6th July 2005, 10:30 PM

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Calculation of sigma from DPMO for defects < 55 %

1st August 2008, 05:27 PM

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Re: How to calculate the sigma level of a process and Relationship of DPMO
Quote:
In Reply to Parent Post by Tim Folkerts
That pesky 1.5 sigma shift sure makes life difficult! And the question of what an "opportunity" is!
There is a "Sigma calculator" you can use at
http://www.isixsigma.com/sixsigma/si...asp?m=advanced
If you have a situation with...
* 83934 units
* 3432 defective units
* each unit is 1 opportunity
Then you have 4.1% defective = 41,000 DPMO. The calculator above says that if the process is centered then this is a 1.74 sigma process. Using the "standard" 1.5 sigma shift says this is a 3.24 sigma process. (these numbers aren't too hard to come up with  they assume a normal distribution that would produce a similar number of defects at the closer spec limit.)
If you considered each test as an opportunity, then you would have 8 times as many opportunities, and a correspondingly better sigma value.
For the example you gave, with xbar=100, limits at 90 & 100, and sigma = 1.8, you are currently (110100)/1.8 = 5.56 sigma from the closest spec limit. However, since the "standard" calculation assumes that the process might drift 1.5 sigma, i.e the center might drift by 1.8*1.5 = 2.7. You would then be only (110  102.7)/1.8 = 4.06 sigma from the closer spec limit. This would, I believe, be the "official" sigma level for the process.
Tim F

I cant accept your apreciation as simple as you say
If is a continuous process, How do you calculate DPMO ..... its depen of the kind of the testing, testing frecuency ........... for me yield must be equal to sigma levels in cetered, normal distribution variable ................... if that we can use the same formula said (Upper Level less media)/sigma.......... we must say exactly what we got real in our process and it work for us ........ theory is not required please...... I dont know if you get my email but is carlos.delgado@ca.sabmiller.com and cdelgadonieto@yahoo.com........... whenever you want to dicussed it please send it ....... if you know about 6sigma and know your process we can learn join
Best regards
Carlos Delgado

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