# Negative Sigma Value

Six Sigma – iSixSigma Forums Old Forums Software/IT Negative Sigma Value

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• #26808

venkatesh
Member

I was reading a recent 6 Sigma case study and the author memntioned that the baseline value of his process was -1.3 Sigma. What is teh significance of a negative Sigma Value? I was under the impression that we dont go below Zero Sigma to denote a process. Can someone throw some light?

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#65130

Participant

Once the sigma value goes negative your PPM defects/defective goes
past 500,000 PPM or 50% Adam

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#65131

Don Strayer
Participant

Really?  500,000 DPMO is 1.5 sigma.  To go negative there would need to be more defects than opportunities.  That would indicate something fundamentally wrong with the way you’re counting them.  In fact, the standard formula cannot even calculate a result when defects exceed opportunities.

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#65132

Don Strayer
Participant

Well, I must add a correction.  I was curious why this question even came up so I did some quick research and found that, yes, the standard formula does give a negative result when the defect rate approaches 100%, such as 950,000 DPMO.  A discussion that occurred in 2002 on the main forum provides some insight, especially message 18482 posted by KMB on September 26.

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#65133

Pallab
Participant

Venkat,
I suggest you look at the basic core definition of sigma instead of looking at at what DPMO level sigma start going negative, thats not the right approach.
The basic definition of sigma level of a process is very statistical, it is :
If you have single spec limit :
‘The number of standard deviation that a process can accomodate between the process mean and nearest customer spec limit.’ (USL-Mu)/SD or (Mu – LSL)/SD. Now simply, when on an average(mean) your process has gone above the upper spec limit or come below the lower spec limit(which ever is applicable to your process). This is the area left of USL or right of LSL.
Both spec limits are available :
Then we calculate the Z bench : that is we calculate both are areas and add them up.
Z=0 essentially means, the yield <= 50%, it cant be more.
Also sometime you will see on articles or case studies, that mean is more than USL (or vice versa), still they are reporting a positive sigma level, dont be confused,  in that case, they have reported short term sigma which long term + 1.5 (generally).
Note, all your sample data/calculation always give you long term sigma value.
Hope this helps.
Pallab.

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#65134