# Why Is 6 Sigma Better Than 3 Sigma ?

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• #52088

Sigma Novice
Member

Why is 6 sigma better than 3 sigma ?
I understand that 6 sigma is 3.4 DPMO and that 3 sigma is 66,800 DPMO but surely being 6 standard deviations away from the mean (or what the customer wants) is not good. This means that you have a wider range of variation doesn’t it ?
For example, if a customer has a requirement for a bolt length to be 2cm and the following values (cm) are produced the standard deviation is 1.34 (the mean of the data set being 2.7cm)
PRODUCTION RUN ‘A’ : 4,1,2,2,1,5,2,3,4,3
Assume now that the following lengths are produced (only the first length changes, from 4cm to 10cm);
PRODUCTION RUN ‘B’ : 10,1,2,2,1,5,2,3,4,3
The standard devaition is now 2.67 (and the mean of the data set is 3.3).
Now, if we assume that 6 sigma (or 6 standard deviations from the mean) is better than 3 sigma (or 3 standard devaitions from the mean) then are we to assume that Production Run ‘B’ is better than Production Run ‘A’ (2.67 -v- 1.34).
How can this be? Production Run ‘B’ appears to be further away from the customer requirement of 2cm ?
Any clarification would be appreciated.

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#182671

Natanyahoo
Participant

You are completely confused.I suggest that you read the basic before jumping into wrong conclusions!

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#182674

Brijesh Agarwal
Participant

Dear,
Your Interpretation is wrong due to:
1- In case 1 the data are normally distributed, P-value is 0.447 & for 95% confidence Interval for mean you will get 1.7432 cm to 3.6568 cm.
2- In case 2 the data are not normally distributed, P-value is 0.017 & for 95% confidence interval you will get 1.3909 cm to 5.2091.
From the above it is very clear that case 1 has less variations than case 2.
Brijesh

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#182689

BritW
Participant

A 6 sigma level, in basic terms, means you can fit 6 standard deviations between a mean and the closest spec limit.  If you can fit 6 SD’s between the mean and spec, then the SD is much smaller than it would be if you could only fit 3 – meaning the process has much less variation at the 6 sigma level.
You need to understand the difference between sigma level (Z value from the normal distribution) and sigma (the greek symbol for standard deviation).

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#182690

GB
Participant

Brit!   Simple, concise, correct…
Long time, no see -hope you are well.
Heebee

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#182691

Stevo
Member

The advice of the previous gentlemen and lady (HB) is for the most part right.  However, look deep enough and we can prove your theory.

Lets say you are taking a test that is graded on a curve. If you score a 99.99966% on it, two linebackers and a defensive end will flunk and you end up getting the snot beat out of you.  But if you score 93.30%, everyone passes and you live another day.  Well, then I believe that 3 sigma is better then 6 sigma.

Always here to help,

Stevo

Ps.  Go Gonzaga!
Pss. Boo North Carolina!

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#182692

Sloan
Participant

Sigma Novice,
Part of your confusion might come from the overly simple example that you gave. You stated that the customer’s specification for bolt length is 2cm. What you actually gave was the customer’s target specification, but you did not give the customer’s upper and lower specification limits. A customer will gernerally have a specified tollerance range around their target spec. For example, your customer may specify a bolt length of 2cm +/- 0.6cm.
Does that make more sense to you?

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#182693

Mikel
Member

As always, your logic is impeccable.
Go Spartans.

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#182694

GB
Participant

Stevo, I agree w/ Stan..Right on!
Go Cats!

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#182695

Sloan
Participant

Stevo,
I like your theory on test grades. I think that must be why North Carolina can’t seem to field a strong football team.
However, BASKETBALL is a different story!
Boo Gorganzaga (sorry, I always get them confused with the cheese)
Yea Tarheels!

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#182702

BritW
Participant

Thanks!  Small hiatus.  Hope you and yours are well also.

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#182706

Hal Frezik
Participant

Mikel Harry has recently shown that 6 sigma is actually a statistical correction to what should have been 6.2 sigma.  It also changes the metric from 3.4 to 3.43 dpmo.
Anyone who is serious about quality and accuracy should implement these corrections.

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#182707

Sloan
Participant

Oops, Hal, you went the wrong way. 6.2 sigma is only 1.3 DPMO not 3.43. Dr. Mikel would not be pleased. Does this mean that you’re not serious about quality and accuracy?

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#182708

Participant

I’ve always stumbled over “3.4 dpmo” – I understand the “spirit” or intent of the mesure, but isn’t “A Defect” a discreet measure?
I can’t have 3.4 smashed pumpkins in my delivery of 1 million.
Non-BB/LSSers are probably more familiar with “Five-9’s”  (99.999%) – which is a bastardized way to describe it quickly.

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#182713

Sigma Novice
Member

If you are confused then think of it this way;
3 errors per 882,353 occurances !

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