# statistical six sigma impretation

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• #28630

i’m working on a project. it deals with motorola inc. i got problems in understanding 6-sigma.
why 6 sigma indicates the lowest defect i.e 3.4 defects per million?
we should have the highest variation for that because it is multiply by 6.
why when we multiply by 5 the variation increases i.e 233 defects per million?
-B.A (Accounting) Hons. Student

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#71581

Hi,
Probably you did n’t get the right concept of six sigma. Six sigam implies that you are able to incorporate 6 std deviations in between your target (center) to the closet specification limit. Now when you say 5 sigma implies you are able keep 5 stad deviations in between your target and closest specification. This implies that your std deviation is increased which in turn means more no. comes out of specificaitons. Hope this gives you some idea.
regards
sridhar

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#71582 A Friend
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Picture this:
A process specification that identifies the lower and upper spec limits (LSL & USL). The target is exactly midway between these spec limits.
Six Sigma Situation:
The observed process data follows a normal distribution such that, when centered on target, the LSL falls exactly at (mean – 6*sigma), and the USL falls exactly at (mean + 6*Sigma). By sigma I mean the standard deviation of the normal distribution. This distance between the mean and the spec limit IS the famed Six Sigma.
When centered on target, the expected defect rate will be only 2 PPB (Parts Per Billion). IF the distribution shifts 1.5*sigma away from the target, one tail will have essentially zero defects – the other will have 3.4 PPM (Parts Per Million) defects. The combined defect rate is (0 + 3.4) = 3.4 PPM. THAT’S how Six Sigma is related to 3.4 PPM.
Five Sigma Situation:
Suppose the data’s distribution is a little wider. Now the spec limits sit exactly at +/- 5*sigma.Keep in mind that the specs didn’t move – sigma got a little larger, so it takes fewer to span the distance from the mean to the spec limit.
If the distribution is centered 1.5*sigma away from the target (midway betweeen specs), We still expect essentially 0 defects in one tail, but in the other tail (remember the distribution for Five Sigma is wider than for Six Sigma) we expect 233 PPM defect rate.
In general, the Sigma number represents the distance between the target and the spec limits, in terms of the process standard deviation (sigma).
In general, the respective defect rate (PPM or DPMO) is determined by shifting the distribution 1.5*sigma to one side – it doesn’t really matter which direction you shift – and then combining the areas under the tail to the left of the LSL and under the tail to the right of the USL. This area will be a probability (less than 1). Multiply it by 1,000,000 to get the respective defect rate.
As the defect rate decreases the Sigma level increases. You can use the Sigma Calculator in the https://www.isixsigma.com website to determine Sigma from DPMO.

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