# Six Sigma – Bell Curve

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• #48681

Anoop Nair
Participant

Is a Six Sigma process +/- 3 Sigma (Total of 6 standard deviations) on a bell curve or +/- 6 Sigma (total of 12 standard deviations) on a bell curve?

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#164833

Dr. Scott
Participant

Anoop Nair,
Six sigma is +/- 6 standard deviations between the mean of your bell curve and the nearest specification(s) for the process. I am not sure why you are referring to the bell curve. Your sigma level is simply the minimum of USL-Mean/S or Mean-LSL/S.
I hope that makes sense.
Regards,
Dr. Scott

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#164835

Anoop Nair
Participant

Dear Dr. Scott – Thank you for your reply. I think I did not articulate my question very well. Assuming I have a Six Sigma process and I have an LSL and a USL, how many standard deviations would I have on either side of my mean? In other words, what would be the Z-value on each side of the mean. Thanks again for your help.

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#164838

Dr. Scott
Participant

Anoop Nair,
Apparently I articulated even less effectively than you did. :-)
You would need at least 6 standard deviations between your mean and either the USL or LSL. In other words, if your process is perfectly centered on the target (i.e., you process mean is the same as your target), then you would have to have 6 standard deviations of space between your mean and the USL and 6 standard deviations space between your mean and the LSL.
Does that clarify things?
Regards,
Dr. Scott

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#164867

Anoop Nair
Participant

Perfect . Thank you!

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#164872

Dr. Scott
Participant

Anoop,
You are very welcome. Hope I helped.
Cordially,
Dr. Scott

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#164873

Erik L
Participant

Anoop,

While the technical definition for the sigma level of a process is the number of standard deviations that exist between the processes average and the closest of either the upper/lower specification (assuming that we can count of 6 increments before the limit) the projection of the VOP is still the normal curve at +/-3 standard deviations from the average (explaining 99.73% of the expected outcomes).

Sigma levels of a process provide a capability assessment and are integrating both VOC and VOP.  Standard deviations are used to portray the expected variation of the process and are a reflection of the VOP.

Regards,
Erik

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#164888

Participant

Good  question:the  second  one

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#164897

Anoop
Participant

Dear Eric – Thanks for your note. I think I understand using Sigma as representing process capability and standard deviation explaining variation in the process. The question that I had was that if we look at the bell curve having the mean equivalent to the target, how many standard deviations on either side needs to be fit to depict a Six Sigma process. I understand from Dr. Scott reply that it has to be six standard deviations on both sides (ie, a total of 12 standard deviations). Put another way, if I have the classical bell curve with mean=target, with 3 standard deviations on either side of the mean  with Z=-3 coinciding with the LSL and Z=3 coinciding with the USL, explains a 3 Sigma process and not a Six Sigma process.
Thanks and Regards,

Anoop
PS: The reason for posting this question was that I had somebody looking at this classical bell curve and telling me that it represents a 6 Sigma process and my argument was that it represents a 3 Sigma process. I hope with the answers that I got from you and Dr. Scott, my understanding is right!

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#164899