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New to Six Sigma Sigma Level Sigma Performance Levels – One to Six Sigma

Sigma Performance Levels – One to Six Sigma

When learning about Six Sigma, it may help to consider these charts, which detail how sigma level relates to defects per million opportunities (DPMO), and some real-world examples.

Sigma Performance Levels – One to Six Sigma
Sigma LevelDefects Per Million Opportunities (DPMO)

What Would This Look Like In The Real World?

It’s one thing to see the numbers and it’s a whole other thing to see how it would apply to your daily life.

Real-world Performance Levels
Situation/ExampleIn 1 Sigma WorldIn 3 Sigma WorldIn 6 Sigma World
Pieces of your mail lost per year [1,600 opportunities per year]1,106107Less than 1
Number of empty coffee pots at work (who didn’t fill the coffee pot again?) [680 opportunities per year]47045Less than 1
Number of telephone disconnections [7,000 talk minutes]4,8394670.02
Erroneous business orders [250,000 opportunities per year]172,92416,6940.9

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why do you mean 3.4 ppm as six Sigma


3.4 ppm means that the opportunities or likelihood that the product/process will fail is 3.4 in a million. like for an instance when you bought a single lottery ticket. the chances of winning is only 3.4 out in a million or 0.00034%. in terms of defects the chances that the single product/process fails is only 3.4 out in a million. it is totally different of saying that producing one million parts you are expecting 3.4 defects which a lot of people misinterpret.


so, im actually going to use real odds from a colorado state lottery ticket. Id like to use Factual Data printed on the ticket just to use real-time data, instead of the defined values of level 6 Sigma Quality.

360,342 winning tickets of 1,800,000
odds of winning a top prize 1 in 600,000
odds of winning overall 1 in 5

so we can say that chances of winning a top prize jackpot is 2tickets per 1.2million sold.
now just quick rough estimate to calculate a value for ppm would be approx 1.8 ppm
so purchasing one colorado lottery scratch ticket, your odds of winning a top prize is 1.8 in 1million tickets, or 0.00018%.

now lets just say, if colorado lottery had a “Scratchology” department which is designated for the sole business of the scratch ticket games, and this was the only scratch game the colorado lottery offered at that time. now lets say they implimented and assembled a GreenBelt project team, gathered key metrics to calculate a DPMO score. lets say, they wanted to see what the DPMO is for the process of printing the scratch games, which consists of taking all the pre calculated data of how many tickets to be printed, and what information needs to be transferred on each individual ticket, with a covert and classified manner. now lets say they werent perfect, but were able to determine that the process has 3.1DMPO. A level 6Sigma quality production line.
now is it correct to say that 3.1 tickets failed to print out of one million tickets printed.

i hope my interpretation of the above information makes sense, and for the most part correct.

Because what stood out to me, is how you gave the lottery odds as a perfect way to differentiate ppm from DPMO. But seeming how they are alike, but not the same, though do have common denominatating value of units, can these numbers used in tandem, or is one apple, the other orange.

if the DPMO figure was factual data, and not the random value i came up with for my perfect example, would it be safe to say, that a computerized production line that printed Colorado Lottery Scratch Game Tickets, did so with a 3.1DPMO, and level 6 excellent, and not just of good quality. and then add that this game not only looks beautiful but it also has a 1:5 overall winning odds, then odds of winning a top prize jackpot is a 1.8 ppm. is it safe to compare the ppm to DPMO, cause id say the printing process is extremely flawed if the DPMO exceeded the ppm of odds of winning yop prizes. if theres the chance that the defectedtickets that didnt print could actuallt be the top prize winners, and change the odds of winning to odds of losing.


why can,t we say that seven sigma or eight sigma instead of six sigma? or explanation of Six?


We CAN use 7 Sigma, but by accident the “lore” developed as 6 Sigma
There is no fundamental law that dictates either
Air travel is approximately a 7 Sigma process

Bharat joshi

Six sigma 3.4 ppm mean 3.4 defect per million opportunity.

It means 99.99966 % data falls withing specification. so that 100-99.99966=0.00034% = 3.4 ppm


no wrong !, 3.4 doesn’t mean 0.00034% defects or 99.99966% good
6 means 99.9997 % good
and there are six [6] sigma levels not 3.

calculated as
[ defect units / (no. of oppertunities * no. of units) ] * 1,000,000


But U know that in calculating of actual capability metrics the normal distribution is from -3s to +3s (centered process). In there are about 99,….% probability of execute products is six sigma level quality. So, from -3s to +3s there is 6 sigma. I must say that in banking exist 7 sigma level.


Thank you for your comments. I see that Six Sigma represents a measurement for the number of defects in a near perfect level of performance in anything we can do.


Defect counts are like random variables representing deviation from mean. They follow bell curve (normal distribution) and have a mean (mu) and a standard deviation (sigma) like any other random distribution.

By counting defects per million you can judge the quality maturity of your process in units of one two three or six times the standard deviation (sigma).

1 2 3 6 sigma = 68% 95% 99.7% and 99.9999998% (percentage of total area under normal bell curve)


How you calculate 1sigma=690,000, 2sigma= 390,538 etc.? Is there any formula?


So Beautifully n simply expressed – so easy for commoners – Gr8


Are you sure about those numbers? 67% failure rate at 1-sigma?
the tails should be 16% each side at 1-sigma
and 0.6ppm at 5-sigma, not 233ppm

I get these:
N NORM.DIST(N,0,1,TRUE) 1-this 2*1e6 x that
1 0.841344746 0.158655254 317310.5079
2 0.977249868 0.022750132 45500.2639
3 0.998650102 0.001349898 2699.796063
4 0.999968329 3.16712E-05 63.34248367
5 0.999999713 2.86652E-07 0.573303144
6 0.999999999 9.86588E-10 0.001973175

Bonkers is right

I got the same answers as you did. So here you are taking the normal CDF (so we get the area except for the right tail above N sigma), and then we do 1-normalcdf(N) to get one tail area, and then 2*tail_area to get the area of both tails, then multiply by one million to get ppm. I am having trouble working backward with a single formula to get all the ppm levels as shown in the article.

Marylou Karkow

MD said I had 2 S.D. chance of death after 5 Years ( 1985); 3 SD (99%) in 10 years (Y2K). As I am still living, how many SD’s am I now?

Junior Faka

Perfect explanation



Why six sigma is calculated in million only and not in billions?

shankha shubhra goswami

everything is ok but the main question is why 3.4defects is rated as 6sigma? why not 5defects or some other value? how the 3.4 value is coming and why it is rated as 6sigma? pls help me. i will be grateful to you. and also explain how to calculate sigma rating from no.of defects

shankha shubhra goswami

suppose there are 50,000 inspected parts and among these 150 parts are found to be defective. so what is the sigma rating for these and how to calculate it? pls help me.

Lathesh mk

Hello Kristine,

Where do we get “Sigma Performance Levels – One to Six Sigma”


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