What does Sigma really mean?

Six Sigma has come to mean a quality management process, but “sigma” is actually a useful measurement of the repeatability of a process.

With the popularity of Six Sigma management principles, it’s common to find metalworking industry professionals, even quality professionals, who don’t know that the lowercase Greek symbol sigma is actually at the core of all modern quality processes.

We know it’s important, but why? Here’s a very brief explanation of what it is and why it matters.

It starts with a histogram:

Take any single measured attribute, from the diameter of a machine shaft, to the weight of an orange; if you are measuring large numbers of that single attribute, there is a simple and powerful mathematical technique that’s the basis for quality metrics in production.

As an example, consider the length of a simple mass-produced part, a nail. Nails are commonly wire-cut and have cold formed heads, so it’s reasonable that controlling the overall length is worthwhile both for customer satisfaction reasons and as a cost control measure.

Inspectors could use vernier calipers or micrometers to randomly check lengths, but unless the dimension falls consistently out of spec, it’s a judgment call about whether to take corrective action.

If we set up an inspection process that takes numerous length measurements however, it’s possible to do something very useful with those measurements.

Now imagine taking multiple length measurements, perhaps two or three hundred.

Starting with our initial value of 1.574 inches, we could put each nail we measure into a cup labeled by length.

The first nail would go into the 1.574 inch cup, the next might go into a cup labeled 1.569 inches, until we had a row of cups holding nails with a range of lengths.

Now the interesting part begins. If we draw a chart (which statisticians call a histogram) with the lengths taken from the labeled cups on the horizontal axis, and the number of nails in each cup on the vertical axis, we get a chart that looks like a collection of vertical bars.

Notice that most of the measurements are close to the 1.575 “bin” and the number of nails with longer or shorter lengths tails off as we go farther away from the centre. Now imagine that we used a much higher resolution instrument than a vernier caliper and had hundreds of paper cups to make hundreds of closely-spaced columns on the horizontal axis.

We could draw a line connecting the tops of the columns to get what mathemeticians call a “Gaussian distribution”, but we know as a ‘bell curve”.

We also know how many nails we have and the length of each so we can easily calculate the average length and note it on our bell curve chart. To make use of the bell curve, we can calculate something called the “standard deviation from the mean”, which is simply a measure of how many nails are a certain distance away from the average length, which for our example is the tallest column in the histogram.

The math isn’t important in this discussion, so we’ll jump to the answers.

One “standard deviation”, which the mathematicians call “sigma” is a range that holds 68.3 per cent of all the nail lengths, both above and below the average length.

RELATED: View from the floor: The religion of Six Sigma

A two sigma standard deviation includes 95.5 per cent of the nails, while a three sigma covers 99.7 per cent, almost all of them.

Go out to the six sigma level and we’re including 99.9997 per cent of the nails.

From a production perspective, if the average nail length is your print spec and the upper and lower limits on nail length fall into the one sigma band, you’re making 68.3 per cent good parts and 31.7 per cent rejects.

At the three sigma level, it’s 99.7 per cent good, so you’re rejecting only three parts for every 1000, which is pretty good.

At the six sigma level, you’re almost perfect, with only three rejects in 100,000 nails produced, which is really excellent quality.

The interesting thing about this kind of analysis is that it applies to any normal measurement of almost anything, from the diameter of reamed holes, to the height of Canadian kindergarten kids. For a normal population of measurements, the bell curve is always there.

What makes “six sigma” the magic word in quality circles is that for most production processes, with 99.9997 per cent of parts close to the average value, if the average is the same as your print spec, it essentially means “zero defects”.

There are two key “takeaways” from this concept. The first is that the bell curve isn’t something you can eliminate, it’s a natural law of nature.

The idea is to make the curve tall and skinny so the six sigma level (or whatever level you need) is as close to the average measurement as possible. The second point is that this method measures how repeatable your process is, not how accurate.

It’s very possible to get a great six sigma distribution, but with all the parts out of spec. Sigma is the standard deviation from the average measurement, which is not necessarily the desired measurement!

If you use automated measuring in your production process, the numbers you need are already at your fingertips.

Compared to conventional control charts, it’s a great way to visualize the variability of almost any production process.