six sigma
Message posted by Art Tully on March 1, 2000 at 12:00 AM (ET)

What percentage of a normal distribution is included in a range of +/- 6 standard deviations?

READERS RESPOND:
(In chronological order. Most recent at the bottom.)

Re: six sigma
Message posted by Bill on March 2, 2000 at 12:00 AM (ET)

Re: six sigma
Message posted by Nancy Diehl on March 7, 2000 at 12:00 AM (ET)

1. If you go into EXCEL and use the function NORMSDIST and put the sigma value in ( ), then
it will feed back to you the area under the normal curve to the left of that sigma value.
For example, NORMSDIST(1.96) will give you .975. 1-NORMSDIST(1.96) gives you the area in one
tail at sigma of 1.96 = .025. So to get the area of +/- 1.96 use: =2*NORMSDIST(1.96)-1.
To answer you question of +/- 6 sigma then use =2*NORMSDIST(6)-1. However, you need to format
that cell to at least 12 places beyond the decimal to get .999999998020 or else you will get a
value of 1.00000.

2. Now, the Motorola concept of 6 sigma bought into by many of the quality areas.....
Here's how it goes...... They say that over time you can expect the mean of your process to
shift. In fact, it will shift as much as 1.5 sigma. Hence the +/- 6 sigma with the 1.5 shift
is actually 7.5 sigma in one direction and 4.5 (6-1.5) sigma in the other tail of the distribution.
When you calculate the area under the normal curve at 7.5 and 4.5 sigma - well at 7.5 it's
pretty much equal to zero. If you take the area at 4.5 and multiply this value by a million, you
get 3.4 defects per million. If you believe this scenario then you are saying your process
has the ability to generate defects at only one end of the distribution and not the other.
It's your choice.

I provided explanation #2 because when I often hear the six sigma words it's generally in
reference Motorola 3.4 dpm story.

Re: six sigma
Message posted by Jason on March 10, 2000 at 12:00 AM (ET)

True +/- 6 sigma accounts for about 99.99999% of the area under a normal distribution. But in a process control setting, a process capable of squeezing +/- 6sigmas in the tolerance is expensive and probably engineering overkill.

Six Sigma theorizes that processes are dynamic and change, as much as 1.5 sigma, over time. Therefore, at +/-6sigma with process shift of 1.5sigma, your process average would never be closer than 4.5sigma to a tolerance. And +/- 4.5sigma is an acceptable level of quality. In manufacturing, that is.