# standard deviation vs. sigma measurement

Six Sigma – iSixSigma Forums Old Forums General standard deviation vs. sigma measurement

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• #37103

batman
Participant

Question again:
Is standard deviation measurement the same as the sigma measurement???
The books and material that I read just alludes to this and there’s no definite answer.
Please elaborate and help out a newbie!
-Batman

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#108565

Bob J
Participant

Hi batman,
They are completely different….
The standard deviation is a unit of measure defined by the scatter in the individual measurements.  It is like an inch, foot, pound or any other defined metric except that it is “custom” for a particular set of measurements.  It shows you how much…
The sigma measurement (or Z value) is the number of standard deviations (units) that exist between the mean of the data and the nearest specification.  This is like 10, 50 or 100 inches in a distance measurement.  It shows you how far…
Hope this helps…
Best Regards,
Bob J

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#108566

RubberDude
Member

Batman,
The formula used to calculate Standard Deviation (signified in mathematics as lower case sigma “ó”) has, is, and always will be the same.  The only difference will be if it is population, sample, estimated, etc.
The “sigma measurement” is the number of standard deviations (ó) from the process mean to one of the specification limits.
If data indicates a process mean is 15, and standard deviation is calculated to be 2, if the upper specification limit is 20, the standard deviation is still 2, but the sigma measurement is 2.5.  In other words, 2.5 sigmas will “fit” between the mean and the spec limit.
Hope that helps.

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#108567

batman
Participant

So a sigma measurement (or Z value) relies on the standard deviation and a specification limit?
OK, let me try to define this in my simple layman’s term:
A sigma measurement is the amount of standard deviation from the mean to a specified measurement.
Should I pick up Statistics for Dummy?
-Batman

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#108568

Bob J
Participant

batman,
Spot on…
It would have been much simpler if there had not been the adoption of “sigma” in both contexts….  I wouldn’t jump for the book just yet ;-)
Best Regards,
Bob J

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#108582

batman
Participant

Thanks Bob! Does “spot on” mean like “right on” or “yes”???
Anyway, upon further reading, I’m still confused I think. Here is a text I read in an internet website:
“One standard deviation away from the mean in either direction on the horizontal axis accounts for 68 percent of the people in this group…”
OK. That’s a simple statement that I can understand. But when I go through the manual calculation I get a standard deviation that is equal to 12.8.
What is the relation of the statement (one standard deviation from the mean…) to my manual calculation???
Are there 2 measurements here? Standard deviation A and standard deviation B???? hehehehehe
-batman

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#108588

batman
Participant

I’m trying hard to understand this. Upon further thinking is it like this:
If I calculate the standard deviation of a set of data and come up with 5.7 that is the measurement (5.7 units) that is equivalent to 1 standard deviation. 2 standard deviation is 11.4 units. Am I right?
-batman

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#108590

Bob J
Participant

batman,
Spot on means “you got it!”…;-)
As for the manual calculation bit, there are indeed two measures.  The first measure of 12.8 is the number of units contained in one standard deviation for your data (usual disclaimers for normality etc).  This defines one “standard deviation” in terms of whatever your units are.
If you now go two standard deviations (each 12.8 original units) on either side of your mean (or 2×12.8 = 25.6 of your original units) then you will have bounded 68% of the population (normality disclaimer).  If you establish a specification and find that it is 25.6 units from the mean then you will have a 2 sigma (Z value) process.
Hope this helps…
Best Regards,
Bob J

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#108591

Bob J
Participant

batman,
Right!
Best Regards,
Bob J

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#108593

RubberDude
Member

Holy histograms, Batman…. you’re correct!!
In the post prior to this one, you asked about “one sigma on either side of the mean containing 68%.”  Using the “standard deviation of 5.7” data, I’ll try to explain this further.
You didn’t indicate the mean of the set of data, but I’ll use 102.  In that case, there is a 68% probablility of any output being between 96.3 and 107.7 units.
If your specification limits are, say, 80 and 120, then the sigma value on the upper side is (120-102)/5.7 = 3.16 sigma.  On the lower end, (102-80)/5.7 = 3.86 sigma.
Just keep in mind, when the “68% of the population” stated in your earlier post is not quite accurate.  The 68% is actually a probability of any given “output” falling in the +/- 1 sigma range.

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#108596

batman
Participant

OK. I think I got it now!!!!!!!
hehehehehe….
I was getting confused about the 2 measurements. I will now go back to the bat cave and meditate on this for a while.
Thanks folks!

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#108661

Matt M
Participant

Std Deviation in essence is the average distance of the data from the mean.  Sigma is the number of std. deviations between the mean and spec. limit.

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#108681

Nari Kannan
Participant

As someone who was somwhat confused by this at one stage just as Batman is (still no guarantees :-)), the light blub went on when it was placed more in business terms. The whole idea of Six Sigma is to reduce variation as much as possible in a process to increase predictability. If you get in as much of the Standard Deviations IN as possible, you have achieved this by essentially including more of the population. So the closer it is to 6 Sigma, it means that you have a large (not all) meaningful % of the population that any additional effort is going to have only marginal difference.
Someone correct me if I am wrong!
Nari

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#108685

Mikel
Member

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#108687

Ashman
Member

It is getting very confusing here.   Can one just say that standard deviation is an estimate of the actual deviation of a population, will the actual deviation of a population is called sigma. And can one just say that a sigma measurement is the “Z” value.

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#108688

Mikel
Member

Very strange definition of marginal – I have never seen that one before.

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#108691

RubberDude
Member

“The whole idea of Six Sigma is to reduce variation as much as possible in a process to increase predictability.”
A bold statement, especially the “increase predictability” part.  This is a part of the SS process, but not the “whole idea.”  Let’s face it…  from the CEO, stockholder down to the janitor are ALL in this game for the money.
Otherwise, I have the same question as Stan….. please define “marginal.”

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#108695

Rey
Participant

This is the simple definition of this site:SIGMA:
The Greek letter s (sigma) refers to the standard deviation of a population. Sigma, or standard deviation, is used as a scaling factor to convert upper and lower specification limits to Z. Therefore, a process with three standard deviations between its mean and a spec limit would have a Z value of 3 and commonly would be referred to as a 3 sigma process.Posted By:
Determining sigma levels of processes (one sigma, six sigma, etc.) allows process performance to be compared throughout an entire organization, because it is independent of the process. It is merely a determination of opportunities and defects, however the terms are appropriately defined for that specific process.
Determining sigma levels of processes (one sigma, six sigma, etc.) allows process performance to be compared throughout an entire organization, because it is independent of the process. It is merely a determination of opportunities and defects, however the terms are appropriately defined for that specific process.
Determining sigma levels of processes (one sigma, six sigma, etc.) allows process performance to be compared throughout an entire organization, because it is independent of the process. It is merely a determination of opportunities and defects, however the terms are appropriately defined for that specific process.Sigma is a statistical term that measures how much a process varies from perfection, based on the number of defects per million units.One Sigma = 690,000 per million units
Two Sigma = 308,000 per million units
Three Sigma = 66,800 per million units
Four Sigma = 6,210 per million units
Five Sigma = 230 per million units
Six Sigma = 3.4 per million unitsIn formulae for control limits and process capabilities, sigma is the symbol for Standard Deviation, calculated from the squares of the deviations of measured samples from the mean value (or sometimes by other methods using ‘magic’ numbers). For a normally distributed output, 99.7% would be expected to fall between +/-(3 x sigma) levels.Posted By: Tom
Modified By: Omer Hayyam OZGUVEN

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#182133

Lomax
Participant

This doesnt seem to fit right for me.  I would think the defintions are flip flopped.  From my understanding
Z-score is a measurement of Standard Deviations from the Mean
Standard Deviations are a measurement
Sigma is a designation of the spread.
If Sigma is the measure from the mean, then a 6 sigma process actually has 12 standard deviations from the lower limits to the upper limits?  (sigma as a measurement from the mean, so 6 on each side).  Sigma cant be a measurement from the mean or we have a general terminology problem.
I though that sigma designated the entire spread, the Z-score does indeed designate the number of std deviations from the mean and measurement intervals are referred to in standard deviations.
A Six Sigma process has a Z-score of 3 which is 3 standard deviations from the mean on either side.

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#182145

Schuette
Participant

Neil,
Six sigma is 6 standard deviations either side of the mean.
99.9999998% of your data is under the curve.
Jim

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#182155

CT
Participant

I don’t see it like this and I may be wrong but standard deviation etc is about the shape of your data, height etc, where “6 Sigma as in the methodology” is about how much of that shape fits between your customer specifications.

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#182158

Tuguchi
Member

Somehow Yes!

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#182160

Schuette
Participant

CT,
By todays thinking your are correct, Six Sigma refers to the method rather than a numeric goal.  The idea today is to improve the product/process until it is no longer cost effective to make further improvements.  The goal is the bottom line.
However, originally the six sigma goal was to obtain a failure rate <= 6 sigma around a mean and within the customer specification.  That failure rate was deemed to be 3.4 dpm (with the bogus 1.5 sigma shift).  An actual 6 sigma failure rate is 2 ppb.
As stated earlier, todays goal is improving the bottom line, not obtaining some magic numeric goal.
Regards,
Jim

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#182384

Lomax
Participant

Six Sigma is 3 standard deviations on either side of the mean (total of 6 sd spread) give or take the motorola shift.
reflects the data inside the specifications, all data is under the curve.  The curve is the data

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#182385

Lomax
Participant

CT,
You are correct in that the 6 sigma methodolgy reflects how much of the curve fits between the customer specifications.  Standard deviation, however is a measure of the spread of data as it pulls away from the mean and though it can be partially reflected in the shape of the curve does not directly relate to its shape.  It can still be bi-modal, favor one side or the other (poisson), etc without being an effect of the standard deviation.

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#182386

Schuette
Participant

Neil,
Of course you are correct about data under the curve.  I meant to and should have said data within specifications.
You are also correct when you say this is a one sided measurement.
However, a 6 sixma defect rate is 6 sixma either side of the mean.  That is the only way a 3.4 dpm falure rate (after the bogus 1.5 sigma shift) can be obtained.
If six sigma is 3 sigma either side of the mean, then a process with a 1350 dpm failure rate is a 6 sigma process.
Please refer to Implementing Six Sigma Smarter Solutions Using Statistical Methods, Chapter 1.
Best regards,
Jim

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#182387

Tuguchi
Member

No
It is actually 6 sigma (sd) on either side!

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#182393

Darth
Participant

Well Neil, you have pretty much clinched the fact that you are clueless. As has already been pointed out, Six Sigma is not 3 s.d. on either side of the mean. That statement, along with your nonsense post about ASQ and certifications put you in the category of “Don’t believe a thing he posts”.

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#182404

CT
Participant

Are you having a joke here. Why would you use SD on non-normal data?

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