Negative Sigma
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 This topic has 15 replies, 13 voices, and was last updated 20 years, 5 months ago by Ravi Pandey.

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December 18, 2001 at 10:46 pm #28405
Terry KruegerMember@TerryKrueger Include @TerryKrueger in your post and this person will
be notified via email.Debating with a colleague whether a negative Sigma value is really possible. I take the stance that it most definitely is since it can be mathematically negative (NORMSINV*1). Any thoughts?
0December 19, 2001 at 1:29 am #70667I agree with you. When calculating sigma levels in Excel if the defect rate is high enough I have had a negative sigma score. I guess the real issue may be that if a process is bad enough to generate a negative sigma why is in existence??
0December 19, 2001 at 4:40 am #70672
Jaran S.Participant@JaranS. Include @JaranS. in your post and this person will
be notified via email.Yes. It is possible.
It means that your mean is out of specification limit and most parts produced from the process are rejected.
It can be possible in this world.
There are some processes like this in my company. We rework several times before final inspection and ship it to customer.
Believe or not, we can still make very good profit from those processes.
Jaran S.0December 19, 2001 at 4:18 pm #70692You’ll get a negative Sigma when your DPMO is exceeding 500 000 or when your yield is less than 50%.That is when more that 50% of the area under your process normal cure is outside of spec. Just math.
That’s not uncommon in bad processes.
0December 19, 2001 at 8:36 pm #70698
Tom BlackMember@TomBlack Include @TomBlack in your post and this person will
be notified via email.Terry,
The sigma level is the number of standard deviations between the mean and the closest spec limit in the direction of target (nominal) to spec. If the mean of the process is on the spec limit, there are 0 std devs between them. The sigma level is 0, the Z score is 0 and the defectives are 50% (from Z table). If the mean moves outside the spec limits, more than 50% will be scrap and the direction from the mean to the spec is towards the nominal, or in a negative direction to the intial definition.
So not only can the sigma level be calculated as a negative it has these meanings.
Tom Black, MBB0December 20, 2001 at 6:33 am #70706
Jugal PrasadParticipant@JugalPrasad Include @JugalPrasad in your post and this person will
be notified via email.I really doubt that any process may have negative sigma. Yo may have negative process capability. If you really see the DPMO Vs Sigma curve, you have 100% defects, which means each opportunity is defective. Negative sigma, seems to me as defects more than the opportunity.
0December 20, 2001 at 7:14 am #70710
Peter ÖrtlundParticipant@PeterÖrtlund Include @PeterÖrtlund in your post and this person will
be notified via email.I do agree that Cp value can be negativ. But not the Zvalue. In that case you have to swap your spec limits to the opposite side of the target. Zvalue mat be infinitely low, but not be below 0.Peter Örtlund
(prospective BB :)0December 20, 2001 at 9:21 am #70712
Jugal PrasadParticipant@JugalPrasad Include @JugalPrasad in your post and this person will
be notified via email.If you talk about process capability the Cpk index can be negative not the Cp.
0December 20, 2001 at 9:23 am #70713
Tim ChambersMember@TimChambers Include @TimChambers in your post and this person will
be notified via email.I don’t agree you can have negative sigma, I don’t agree you can have negative Cp, I do agree you can have negative Cpk.
I think this is all driven by how you calculate sigma levels, if calculated from simple 3 x Cpk values, it is obvious how negatives have been generated (i.e. process average outside spec. limits). If generated from absolute inside spec. – outside spec. standpoint you should not go below zero, you could be at zero, but not below.
Taking 1.5 sigma away at these low levels for a coversion to long term results is also false, 1.5 being a simplistic ‘catchall’ figure, different for each process. For example, as sigma levels approached, say, 0.5, the long term effect maybe something like 0.2 sigma, whatever; it would be less than 0.5 – measure it.0December 20, 2001 at 11:03 am #70716
Eoin BarryParticipant@EoinBarry Include @EoinBarry in your post and this person will
be notified via email.I would like to see more discussion about the basis of the 1.5 sigma shift.
I would suggest that the 1.5 sigma shift, which can be really useful, is a gross generalisation and needs to be measured not confused with mathematical fact.
It is a reasonable guess at long term variation, but I’ve never seen any peer reviewed study which backs it up or which attempts to put a confidence interval around it. Does anybody out there know of such a study?
Merry Xmas.
Eoin
0December 20, 2001 at 1:12 pm #70719If you want to learn more about the 1.5 sigma shift, take a look at these other forum posts I found on the subject:
https://www.isixsigma.com/forum/showmessage.asp?messageID=4154
https://www.isixsigma.com/forum/showmessage.asp?messageID=5225
https://www.isixsigma.com/forum/showmessage.asp?messageID=849
0December 20, 2001 at 3:12 pm #70728
Terry KruegerMember@TerryKrueger Include @TerryKrueger in your post and this person will
be notified via email.Tim,
I agree with you – especially on the 1.5 Sigma shift concept. If you look at the definition of Six Sigma as standard deviations from the spec limit, then there should not be a negative sigma, but it should be noted that the standard deviations are on the wrong side of the spec limit. Mathematically this is represented by a negative – although it really wouldn’t be negative. So it is mathematically possible, but not realistic. Do you agree?0December 20, 2001 at 3:43 pm #70732
Dave Simon BBParticipant@DaveSimonBB Include @DaveSimonBB in your post and this person will
be notified via email.Even this depends on whether or not you include the 1.5 sigma shift in your calculation. I believe most companies have bought in to the 1.5 shift, thus you would have to have over 933,800 DPMO to be at negative sigma. I concur with the other comments in that negative sigma would be indicative of a very bad process.
0December 20, 2001 at 4:39 pm #70737
Tim ChambersMember@TimChambers Include @TimChambers in your post and this person will
be notified via email.To be honest – I much prefer the use of Cp & Cpk terms (in conjunction) to describe a process in relation to it’s specification, a completely unambigous method (as long as everyone uses 3 deviations).
I don’t like negative sigma, I prefer conversion of %good (to sepc limits) to sigma level; using +NORSINV() in Excel for example.0December 20, 2001 at 5:44 pm #70740Sigma cant to be negative. If you have 58% scrap, so you ll have 42% Yeld, so you can have sigma considering inverse of normal standard curve.
If you want to go by Cp to sigma, you owe first the percentage of the normal curve between the limits (the Yeld) and then to convert it to sigma. You don’t have to subtract 1.5 since Cp is already calculated in reference to the brief term.0December 25, 2001 at 7:46 pm #70818
Ravi PandeyParticipant@RaviPandey Include @RaviPandey in your post and this person will
be notified via email.I came today to start writing a short note for publication on this issue. Obviously, I am writing this note before. Here is what I have in mind:
1) As per the definition available from the web sites and also from training material, SIGMA value can not only be negative —in fact it can be minus infinity.
2) Since Sigma calcualtion is a matter of definition, there is nothing right or wrong about it.
3) I personally find it unacceptable to use a metric which will give Negative Sigma Value.
4) I think zero yield should equal to zero sigma without the 1.5 shift or 1.3 multiplier.
ravi Pandey0 
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