3 or 6 StdDev
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 This topic has 15 replies, 8 voices, and was last updated 13 years, 8 months ago by Mikel.

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August 27, 2008 at 11:30 am #50825
Question: When a company asks you if your process is Six Sigma, do they mean Plus/Minus 3 StdDevs or Plus/Minus 6 StdDevs
0August 27, 2008 at 11:55 am #175224Deka:
+/ 6*S within the specs chosen by your customer where S is short term Sigma (=> Cp=2)
(+/ 3*S covers 99.7% of the data and corresponds with Cp=1)
+/ 4.5*S if S = long term Sigma (the 1.5 Zshift is then incorporated => Ppk = 4.5)
0August 28, 2008 at 6:25 am #175259
Ravi KanthParticipant@RaviKanth Include @RaviKanth in your post and this person will
be notified via email.Hi,
Put simply, its +/ 3 sigmas(standard deviations) on either side of the mean value.0August 28, 2008 at 11:59 am #175266I may be way off base, but I want to challenge that. If Sigma is related to z score and z score looks at a one sided dist. I beleive you just described a 3 sigma process. I think Six Sigma is +/ 6 Std Dev from the mean, related to a normal dist
0August 28, 2008 at 12:22 pm #175269
NameWithheldForSafteyParticipant@NameWithheldForSaftey Include @NameWithheldForSaftey in your post and this person will
be notified via email.I may be wrong but…..
I think your confusing two things here.
Standard Deviation tells you how much variation you have in your process where as your sigma score tells you how you perform compared to your customers operating limits.
So what they’re asking is now many errors do you have in your system? 6 Sigma generaly known as being 3.4 defects for every million opportunities to make a defect.0August 28, 2008 at 12:57 pm #175272
Bill FowlkesParticipant@BillFowlkes Include @BillFowlkes in your post and this person will
be notified via email.Six Sigma really means that a product is produced in a high quality manner such that it’s components have a failure rate of 3.4 defects for every million opportunities to make a defect.
All the rest, such as +/ 6 stn.dev. depend on the details of the governing distributions and statistical behavior.
By the way, Ravi is flat out wrong, +/ 3 sigma is not correct.0August 28, 2008 at 5:04 pm #175282
Jonathon AndellParticipant@JonathonAndell Include @JonathonAndell in your post and this person will
be notified via email.I agree with your concenr. The “process sigma” is the number of standard deviations between the mean and the NEAREST specification limit.
0August 28, 2008 at 7:58 pm #175289I understand the connection between Z score and Sigma Level..but my thick head cant connect the dot to Std Dev and Sigma Level. Most tables list DPMO, Sigma, and CPK together, but not Std Dev.
0August 28, 2008 at 9:01 pm #175291
Jonathon AndellParticipant@JonathonAndell Include @JonathonAndell in your post and this person will
be notified via email.For continuous process data the Z score simply counts how many standard deviations fit between the mean and the nearest specification limit. That computation depends on three things: 1) the value of the mean (XBar), 2) the gap between mean and specification limit, and 3) the value of the standard deviation (s). No doubt you have seen the equation a zillion times.
If you improve the process by making “s” smaller, you will be able to fit more standard deviations between the mean and the specification limit. That’s why small s leads to high Z.
If I failed to answer the same question you are asking, let’s have another go at it…0August 29, 2008 at 9:06 am #175307hai Deka,
here is the ‘formula’ between Sigmalvel (Zlt) and Sigma(lt):
Zlt = 3* Ppk = Minimum(USLMu,MuLSL)/Sigma(lt).
This is the same as what Jonathan said, but in mathematic language.
– USL and LSL arer the specs the Customer has wished for. Mu you don’t know but you fill in Xbar Sigma(lt) you don’t know but you fill in the Sigma that your customer typically will see (all longterm variation included; whatever the causes)
Remi0August 29, 2008 at 3:10 pm #175316Understood. Now… If the Z Score and associated sigma level are based off of the nearest spec limit and your data is slightly moved to the right (for example). How are all of the defects that are on the left (below the Lower spec limit) accounted for? They cant be ignored?
0August 29, 2008 at 3:24 pm #175317Hai Deka,
they are not accounted for with Cpk, Ppk or Zlt or Zst. They are accounted for by Yield%, Reject% and a SixSigma term called Zbench.Zbench is a translation into Six Sigma language (sigmalevel) from Yield%; in the same way that Zlt is a translation of Yield%attheworstspec. What you do is calculate total yield% and transform into Zvalue. minitab can do it automatically if you have data (Stat>CAPAN; options: “Zbench instead of Ppk”). There is also a way to do it if you only know Yield% + Nomality.
And ofcourse with Zbench you also have the Zshift dilemma (compensate with 1.5 or not). Other threads discuss this dilemma in detail.
In Improvementprojects in general Zlt gives you a good indication of how good your process is: “the other side is better so improve this side first””. If the process is centered Zlt corresponds with half the Reject%.
Remi0August 29, 2008 at 4:39 pm #175319
Jonathon AndellParticipant@JonathonAndell Include @JonathonAndell in your post and this person will
be notified via email.In some instances the tail beyond the nearest spec limit has virtually all of the defects. For instance, suppose the mean happens to lie 2 standard deviations from the upper spec limit, and 4 standard deviations from the lower limit. This means there is about a 2.3% likelihood of a defect beyond the upper limit, but only a 0.003% likelihood of a defect below the lower limit – a factor of 70,000 times as many defects in the upper tail.
In other instances, both tails might be important. If Z(Upper tail) is 2, and Z(lower tail) is 2.2, then you have to account for both sides of the distribution.
Most software packages do this by adding both tails’ probabilities together, and computing an “equivalent” Z value that corresponds to that total number of defects.
I have a simple Excel template that handles this. You enter the process mean and standard deviation, along with one or two specification limits, and it computes the Z value. If you send me your email I will send it along. If the “isixsigma powers that be” want to make it available for all, I will be happy to share.
Bear in mind: if the data are discrete, or if continuous data are nonnormal, this template is the wrong one to use. I also have a template for discrete data.0August 29, 2008 at 5:25 pm #175320Jon,
yes..please..send both to:
[email protected]
Great input..thanks0August 31, 2008 at 10:57 am #175332Your process mean is at least 6 standard deviations from the nearest spec limit. It could be 6 std dev from one spec limit and 100 std dev from the other….depending on the location of the mean, and the magnitude of the std dev.
0September 6, 2008 at 6:27 pm #175527Pls send the two Excel charts to me at [email protected].
Thank you.
Stan0 
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