# Relating Number of Standard Deviations to Sigma Level

Six Sigma – iSixSigma Forums General Forums New to Lean Six Sigma Relating Number of Standard Deviations to Sigma Level

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• #55100

leaning
Participant

Hello. Have I got this right?:

A Sigma Level of 1 (-sigma to + sigma about the mean) contains two standard devations, 68.27% of the values, yields 30.9% of good items, and 69.1% of defective items (DPMO 691,462)

A Sigma Level of 2 contains four standard deviations, 95.45% of the values, yields 69.1% of good items, 30.9% of bad items. (DPMO 308,538)

A Sigma Level of 3 contains six standard deviations, 99.73% of the values, yields 93.32% of good items, 6.68% of bad items. (DPMO 66,807)
….

A Sigma Level of 6 (“6 Sigma”) contains 12 standard deviations, 99.9999998027% of the values, yields 99.9997% of good items, and .0003% of bad items. (DPMO 3.4)

(I was getting confused because the curves I see all over the six sigma sites just show the empirical rule (68-95-99). I started thinking that 6 sigma = 6 standard deviations = (-3 to +3). Then I saw one curve on a site that actually went from -6 to +6 (12 standard devations). So, hopefully, I got it right above now. I appreciate your help checking this!

Regards,

Leaning

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#198636

Strayer
Participant

Sigma is the number of standard deviations between the mean and the nearest specification limit, upper or lower. Maybe you’ve been confusing control limits with specification limits. That’s pretty common for beginners. In process control charts we use +/- 3 standard deviations as the control limits. It’s a range of six but very different from six sigma. Control limits are calculated. Specification limits are defined by the customer’s tolerances. We can have a process that’s in statistical control but isn’t six sigma. Hope this helps.

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#198639

leaning
Participant

Strayer,

So how many standard deviations are there for a Sigma Level of 6?

Regards,

Leaning

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#198640

Amit Kumar Ojha
Participant

There are 6 Standard Deviations between Mean and the nearest specification limit for a process operating at 6 sigma level.

So in case both specification limits are present, there would be [-6 to +6] 12 SD between USL and LSL.

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#198638

leaning
Participant

Strayer,

Hmmm..

I found another post here: http://www.qualitygurus.com/courses/mod/forum/discuss.php?d=3273:

Notice the first answer is that there are 6 “sigmas” (the symbol for standard deviation) between the process mean and a specification limit. So that would be 12 total SD’s from -6 to +6. Notice that the second answer asserts something different: that the 6 sigma’s come from -3 to +3 (so 6 standard deviations), not 12.

So on one hand, the “6” in 6Sigma is either talking about 6 sigmas as in 6 standard deviations (-3 to +3), or on the other hand, the 6 is on either side of 0 (-6 to +6). My opinion is that in order to capture everything but .0003%, “6 Sigma” has to mean -6 to +6 (12 SDs) because -3 to +3 would still not capture 6.68% and would have a DPMO of 66,807, not 3.4.

So, you get many different answers to “How many standard deviations correspond to a 6 Sigma Level?” depending on where you look. Fun with Google. :)

Regards,
Leaning

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#198650

BBme
Participant

@leaning69. That reference is terrible because it’s not complete.

Use this one:

It should be clear from this description.

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#198687

Mike Carnell
Participant

@leaning The link you posted is pretty representative of what you can get on forums although typically that close together. The first answer was plain stupid, the second was the same as you gotten here twice and the third answer was for control limits.

@Straydog
gave you the correct answer. @Amitojha basically said the same thing. They are giving you the correct answer.

What I don’t understand is since you are telling us you are tying these percentages, ppm etc back to a Z table why haven’t you asked why 6 sigma doesn’t equate to 3.4ppm? In light of your posts it seems like a rather obvious thing to miss.

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#198688

Mike Carnell
Participant

@bbme Your link should explain it pretty well. The drawing of the curves being centered in the spec is common enough but also feeds the idea that SS is about centering the distribution – which has nothing to do with it.

The comments under the article were hilarious in a very statistician type of way. I did like the one that asserted that Taguchi designs ha been used in agriculture since the mid 1800’s (Genichi Taguchi born January 1, 1924; died June 2, 2012). I guess the split plot designs are easily confused with Taguchi designs?

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