Six Sigma “Sweet Spot”: The Search for A Divine Proportion

Minitab Blog Editor 01 August, 2011

divine proportion

Lately, I've been thinking a lot about the "perfect" proportion. We’re adding a sunroom to our house and debating the best dimensions for the rectangular addition. Naturally, "the golden ratio" is an enticing option.

Also called the Divine Proportion, the golden ratio has gotten a lot of buzz over the centuries. Its basis is simple yet profound.

Take a line segment and divide it into two segments so that the ratio of the longer segment (B) to the shorter segment (C) is the same as the entire line segment (A) to the longer segment (B).

golden line segments

That ratio, which is [1 + sqrt (5)]/2, or roughly 1.62, purportedly represents perfect beauty and balance.

The ancient Greeks recognized the importance of the golden ratio in the construction of the five platonic solids, which they believed to be the essential elements of the universe.
platonic solids
In the 16th century, that ultimate Renaissance man, Leonardo da Vinci, created the illustrations for the first known book on the golden ratio, called de Devina Proportione. Some claim he applied this ratio when creating spatial relationships in many of his artistic masterpieces, such as The Last Supper

If you google around a bit, you’ll see that this rarified ratio pops up a lot in art and aesthetics, even today, including modern reconstructive surgery that attempts to recreate the “perfect” human face!  

This got me thinking…

What if Leonardo da Vinci came back in the 21st century as a Green Belt? 

So instead of painting enigmatic smiles, Leo earned his daily bread creating and analyzing Pareto charts and capability analyses

As a Green Belt, he probably wouldn’t have much use for the classical golden ratio. But he’d still discover a lot of other mathematical “sweet spots”  in his quest for quality.

six sigma

The “Golden Ratio” of Process Performance

You might call this the classic definition of a “Divine Process”: 3.4 defects per million opportunities. 

This is the six sigma standard of perfection, and it means that 99.99966% of your products are statistically expected to be free of defects.  

It even assumes a 1.5 sigma shift over the long-term, giving the process ample elbow room within the specification limits.

How good is this standard? For a vivid illustration, compare it with processes that are only 99% good.  You might not think there'd be that much difference -- hey, we're already at 99%, right? -- but here's how that difference plays out in practical terms:

99% Good 99.99966% Good (6 sigma)
Power outages for 7 hours each month One hour-long power outage every 34 years.
3,900 mail pieces mishandled at the U.S. Postal Service each minute 1.3 mail pieces mishandled at the U.S. Postal Service each minute
52 feet of imperfections on a mile-long bolt of cloth 0.25 inches of imperfections on a mile-long bolt of cloth
106,849 drug prescription errors per day 36 drug prescription errors per day
285 short or long landings on U.S. commercial flights each day One short or long landing on a U.S. commercial flight every 10 days.

Of course, the six sigma standard should be viewed in relation to the realities of your process, your field, and your customer requirements. For some processes with critical, life-dependent products, six sigma may not be good enough. For example, I’ve heard that some in the aeronautical industry are considering using a seven sigma standard.

For other processes, the six sigma standard may be unrealistic or too costly to achieve. In those cases, allowing a higher level of defects may be perfectly acceptable, depending on the nature of the defect.

If you want to assess the sigma capability of a process, you can do it with Minitab Statistical Software. And remember Rome wasn’t built in a day—or a month, or a year, for that matter. So process improvement typically moves in smaller steps toward an ultimate goal, project by project.  

Luckily, there are lots of other “mathematical sweet spots” that you can use to gauge progress in your ongoing quest for perfect quality. Stay tuned.