# 6 - sigma question?

I need to clear up some confusion I have about 6-sigma.
The teachings say that 6-sigma means that in a million opportunities there will only be 3.4 mistakes or "missed opportunties" IF you have achieved 99.997% Perfection.
Or something to that nature.
The concept is based on six standard deviations from the population mean. I'm assuming it means that the sample group's mean is six devations from that population mean.
But what I'm confused about is .."WHAT POPULATION?"

IF a company is building electric motors. They want to acheive an error of 3.4 per million. I'm assuming that 3.4 is the number of individuals represented by the area under the bell-curve out in the extreme fringes of the bell-curve (out in the six sigmas away from the mean).

OKay, I can comprehend population curves (bell-curves ) in terms of animals, plants, human behavior and other human traits, but HOW DOES THE BELL CURVE APPLY TO MANUFACTURING?
6-Sigma was created by Motorolla, explain please!!

The Bell Curve As It Applies To Manufacturing:

Every manufacturing process has parameters associated with it. For instance, if you're making a cylinder bore to a certain length and diameter, then those are two parameters you can track. You can measure the length and diameter of each cylinder bore as it comes off the line.

The concept is that, no two parts will be exactly the same; the manufacturing process has some small deviations from cycle to cycle. Some of this is tolerable, but too much will throw the part out of spec. One way to track this is simple tolerance management--the idea that we'll measure EVERY part as it comes off the line. It's the safest way to ensure quality parts (and plants will revert to this as a fail-safe during a loss of quality control), but it's VERY manpower-intensive. The more manhours you have to pay, the less competitive your piece price is, and the less you profit as a company.

So there's a desire to ensure that every part coming off the line is in spec without measuring every part. Enter, statistical process control, and Six Sigma.

Six Sigma, as you know, dictates whether a process is in control by determining where a sample's measurements fall in relation to the high and low tolerances. The measurements in this case are the values of the parameters you picked for the parts in question. With the cylinder bore, for instance, you'd measure the length and the diameter.

Instead of measuring every part, you measure a sufficient sample of parts out of each lot to determine where the measurements fall in relation to the high and low tolerances. For instance, you'd measure 100 diameters, or 100 lengths, or every sixth length or diameter continuously, and see where they are statistically with each other.

Hopefully your 100 measurements, when plotted on a histogram, will take the measure of a bell curve. That's good, that means the measurements are statistical. Then, figure your mean and your standard deviation. All you've got to do is make sure that you have 3 sigma on each side of your mean, and make sure that those values for 3 sigma are all inside of your high and low tolerances. If you can do that, then your process is "in control".

So, the bell curve in manufacturing is formed by measuring a feature on all of your sample parts. That feature can be ANYTHING--it can be a physical dimension, it can be a critical temperature reached in a process, it can be an amount of material deposited, it can be a length of time spent in a forging chamber...it can really be anything. The only restrictions are that it has to be a bell curve, there has to be a 2-sided limit with high and low tolerances, and you have to have enough samples to qualify as statistical.
I don't have a very strong grasp of the 6-sigma process, but from what I do know, 3.4 is the number of errors per million processes.
My employer uses the 6-sigma process to measure performance in data accuracy. We take fuel orders from commercial customers, and in your example there would be 3.4 mistakes per every 1 million orders. That would be a level 6 sigma, I believe, and it is said that any manual process is unlikely to achieve greater than 4 sigma.
I'm sorry I can't help much. I've posted a few links where you can find more information.
It is the combination of all possible sources of error. It applies to the people, the process in use, what other companies are doing, how they are doing it, errors in judgment, practice, materials, and the up keep of the manufacturing equipment. All of these things play a role is what can go wrong in a process. Some things are controllable, others are not. So, the population is the sum of all possible means of error occurrence. The goal is to minimize what can be controlled in the manufacturing process.

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