Desperately Seeking Sigma

Nominally sigma is the 18th letter of the Greek alphabet.  

The uppercase version is that sort of pointy "E" letter that looks like this:  Σ 
A lowercase sigma looks like a little zero with a cowlick :  σ
When sigma appears at the end of words or sentences it has yet another form:  ς

As we have been amply enlightened by Gritchka and N-Wing in their write ups on Sigma, I won't delve any further into the etymology of the letter itself.  Our interest in sigma lies in exploring what happens when you put six of these sigmas together.  More specifically we'll look into the arcane world of business process jargon, and examine a current corporate management fad

Say hello to the Six Sigma Methodology1.

If you read virtually any popular magazines, it's likely that you have bumped into a strange looking advertisement from Microsoft sometime in the last year.  The ads are all a little different,  but they share the feature of a line of five colored rectangles, each containing a large numeral "9."  The ads may be somewhat opaque to the non-technical viewer, but what Microsoft is referring to is a measurement of quality.  Those five nines in the ad are known in the IT industry as "five nines," and they represent 99.999% uptime, which is regarded as the highest reliability realistically possible with current computer technologies.  99.999% uptime means that your system is down for less than five minutes in a year's time.  

As even the most casual user of Microsoft software2 is well aware, this is a preposterous claim.  Even within the context of normal advertising hyperbole, five minutes a year of downtime is almost impossible to achieve.  Lest it be said that I'm singling out billG and the microserfs for special abuse, let me hasten to add that the five nines are equally beyond the reach of Oracle, or Sun or Linux as well. Speaking as a technology professional with more years on my keyboard than I like to admit to, I don't think there's any general purpose, computing platform that has ever delivered five nines performance over any appreciable period of time.  There's just too much to go wrong.

And that brings us to an even further strain on our credulity, The Six Sigma methodology.

Six Sigma is one of those weird management fads that weird managers seem to glom onto periodically.  Kaizen, Total Quality Management, you've probably seen em come and seen em go.  Combine a little psychobabble, a really compelling PowerPoint presentation and a basket full of breathless claims and you get the next big thing.  Lately, one of the next big things has been Six Sigma, which is commonly defined as 3.4 defects per million opportunities.  I'll drill into the math a bit below, but basically Six Sigma thumbs its nose at five nines.  That sixth decimal point would correspond to an even more unbelievable improvement in reliability, to the point where your total system downtime would amount to less than two minutes per year.  I am so totally sure! 

Why is so important to get things right? (an actual quote from, ach!)

The term Six Sigma is derived from the normal mathematical usage of Sigma as a representation of standard deviation, or the spread of values around a mean or average.  In the context of management-speak, this use of sigma implies the distribution of defects around a zero-defect production model.  In the real world, zero-defects is a nearly impossible goal.  

If you, as an individual, try to make a perfect thing, be it a painting, omelet, or perfect node on E2, you might be able to achieve it.  Depending on the difficulty of your endeavor, it might take five minutes of practice, or a lifetime of careful study.  But, it you were talented, and diligent and, perhaps, a little bit lucky, you might be able to pull it off.  If, on the other hand, you had to do that same perfect thing a million times, your chances of pulling it off would drop to an infinitesimally small number.  A snowball's chance in hell, is the phrase that comes to mind.  And if you had to ramp up to the typical demands of mass production, where you are expected to do that perfect thing millions of times a year, year after year after year.  Well, you get the picture.

So, along comes the Six Sigma consultants, complete with a pretty PowerPoint presentation, and a bunch of white papers, and a consulting contract for your boss to sign.  The snake oil that they are selling is that using their methodology, your company can enter the elite ranks of essentially zero-defect manufacturing.  Hey, the Six Sigma crew has a right to earn a living, and the goal of zero-defect manufacturing is a pretty dream, but what effect does a "well-structured, data-driven methodology for eliminating defects, waste, or quality control problems of all kinds in manufacturing, service delivery, management, and other business activities," have on normal human beings like you and me?

In a word, it sucks.  It radically widens the gulf between management and labor by creating completely unreal expectations on the management side, and slyly loading impossible burdens on the people who are doing the zero-defect work.  Rather than creating any tangible benefits for the company, adopting Six Sigma methodology, often creates an irreconcilable gap between what's expected and what's desired.  It's much easier for management to toss another sigma on the pile, than it is to roll up their sleeves and actually figure out how to prevent that one last defect. As you might imagine, the workers who are responsible for achieving Six Sigma results have a less sanguine perspective on the matter.

Where does the name Six Sigma come from?

The proponents of  Six Sigma claim to trace the term back to Carl Frederick Gauss (1777-1885) who introduced the concept of the normal curve in statistics.  Sigma was first applied as a measurement standard in the 1920's when Walter Shewhart proposed that three sigma (or standard deviations) from the mean is the point where a manufacturing process required immediate attention. The term "Six Sigma" is generally credited to a Motorola engineer named Bill Smith. "Six Sigma" is a federally registered trademark of Motorola.  Six Sigma has been famously (or infamously) applied by Allied Signal and General Electric since the late 1990's.  

You do the math

If one operation in 10,000 fails, then the overall probability of success is 0.9999. So, for example, if it takes five successful operations to create a finished product, and each operation has a 1 in 10,000 chance of failure, then the probability of a product being completed successfully is (0.9999 * 0.9999 * 0.9999 and so on 5 times) = .9995.  To put that another way, the chance of a successful completion is 99.95%.  Since the stated goal of Six Sigma is 3.4 defects per million products, we're looking at 3.4 in 1,000,000 chances of failure or .00034% and conversely, a 99.9997% chance of success.  A more rigorous textbook calculation of six sigma yields an error rate of approximately two defects per billion, or 99.9999998% success rate.  This level of perfection is so vacuous that even the six sigma devotees get nosebleeds. So they add in a generous fudge factor that assumes the mean drifts by up to 1.5 standard deviations.  This assumption lowers the bar to the still unbelievable, but less absurd error rate of 3.4 defects per million3.

To compare all this with Microsoft's five nines, consider that there are 31,563,000 seconds in a year. Now if 3.4 of every million seconds may be defective, that's 31.563 times 3.4 defective seconds or a total of 107 seconds of Six Sigma downtime per year compared with over 300 for the five nines.  Thus Six Sigma clearly demonstrates its superiority over five nines, right?  Only in the fantasy world of management consultants. 

Six Sigma Roles:

So, what happens when your boss buys into the Six Sigma concept and hires a consultant to come in and get all you defect-prone workers on the right track again?  Well, first off, forget about raises for awhile, these Six Sigma guys are really expensive and they tend to make everybody look bad in the boss' eyes.  After all, if you guys were doing it right, already, he wouldn't have to hire them in the first place, right?  

Then one morning Team Six Sigma will show up at your place of business and things will get really weird.  For some strange reason they've adopted a belt-ranking system derived from the martial arts. Here are some examples:

The Champion coordinates a business road map to achieve Six Sigma standards. This person selects projects, executes control, and alleviates roadblocks.

The Master Black Belt is mentor, trainer and coach in the Six Sigma organization.

The Black Belt leads the teams implementing Six Sigma methodology on projects.

The Green Belt delivers successful focused projects using the Six Sigma methodology and tools.

Team Members participate on the project teams and support the goals of the project.

If you are really lucky, you might get an opportunity to go spend a week in some crappy motel in Houston getting your Six Sigma Green Belt certification.


1 International Society of Six Sigma Professionals (ISSSP):

2 Handy Six Sigma calculator:

Microsoft's comments on how reliable their software is:

Spezial Thx to Wrinkly for help with the math!

The Mathematical Flaws of (most) Six Sigma Methods

Walter A. Shewhart was a very bright fellow who came up with some interesting ideas and techniques. These have proven immensely effective when properly applied.

So what the heck is up with Six Sigma? Well, the problem is, these people have taken a number that Shewhart pulled out of his entirely human ass and ignoring most everything he did that was worthwhile. Whether this was ignorance, stupidity, or a little of both is an open question. Now, 3 sigma unit limits to either side of the central line are not without value - but the main reason Shewhart kept them around is because they worked. But they're not based on the Central Limit Theorem. The normal distribution is conspicuously absent. Any figures giving parts per million defective are based upon the assumption of a normal distribution. This is generally all but unprovable, even when correct. It's also not required by the techniques that Six Sigma is derived from. Making a calculation to enough decimal places to give you, say, 3.4 parts per million based on a wild assumption... any good applied mathematician would observe an exponential rise in their own beating you with a big stick behavior.

And as far as five nines vs. six sigma... we're talking about two very, very different things. Five nines is a goal. Six sigma, or rather let's say control charts, are a technique to improve your process. Comparing the two shows a deep and terrible misunderstanding of what Shewhart was talking about. Six sigma should help you strive for that kind of reliability, but they are not the same thing.

Was Enron Really That Surprising?

At my school, only business majors are required to take Making Moral Decisions. You'd think they could at least figure out running a business, but from the sounds of thing, that math geek Shewhart had 'em beat - or at least the Six Sigma goons. He talked almost as much about using his techniques in a reasonable manner in the real world as he did about the math itself. He's very vehement about working towards improvement, not some arbitrary goal which is very likely not even achievable with the current process. Shewhart's limits are set based on the natural variation of the process itself - not the specifications handed down by someone who's probably never seen the factory floor, tech support farm, or whatever the process might be. Management is supposed to work with and for workers - I've read countless examples of this working perfectly.

Six Sigma and the McDojo Phenomenon

Young one, study the ancient and powerful teachings of the old masters. They will allow you to defeat many enemies with your great power! When you have learned all that there is, you will be given your black belt and you will be unstoppable!

McDojo - a term often applied to martial arts training centers that promise you the world, deliver little to nothing but the outside form, take your money, and run away cackling. I'm surprised the Six Sigma folk had the brazen nerve to adopt a colored belt system to their... teaching. It makes the comparison almost too easy. They attempt to tie their techniques to some ancient foundation, rather than allowing them to stand on their own merit. They have adopted some of the outer appearance - six sigma units - but not the core ideas that made the original techniques powerful. Heck, half of them may not even know how wrong they are.

A black belt, I should add, generally means you've mastered the basics of an art and are ready to move on to deeper understanding. And heck, even then, it doesn't mean anything except to you and your teacher. Six Sigma units are just a certain range Shewhart made up that seem to work effectively and economically. There. That's it. I grant you your Six Sigma Bling-do Black Belt. Go read a book on statistical process control and promote yourself up to however many stripes you want. And if you really want to improve your business, go buy a book like Wheeler and Chamber's Understanding Statistical Process Control. Our class worked from this book in the SPC course I took, where I learned most of what I've just talked about. Unless you start getting into the stuff in the back (that you don't need anyway), it's really pretty understandable and easy, even if you're not mathematically inclined.

A shepherd was herding his flock in a remote pasture when suddenly a brand new BMW advanced out of the dust cloud towards him. The driver, a young man in a Broni suit, Gucci shoes, Ray Ban sunglasses and a YSL tie, leaned out the window and asked the shepherd, "If I tell you exactly how many sheep you have in your flock, will you give me one?"

The shepherd looked at the man, obviously a yuppie, then looked at his peacefully grazing flock and calmly answered. "Sure."

The yuppie parked his car, whipped out his computer notebook and connected to a cell phone. Then he surfed to a NASA page on the Internet where he called up a GPS satellite navigation system. He scanned the area and then opened up a database and an Excel spreadsheet with complex formulas. He sent an Email on his Blackberry and after a few minutes received a response. Finally, he printed out a 150-page report on his hi-tech miniaturized printer. Then he turned to the shepherd and said, "You have exactly 1586 sheep."

"That's correct, take one of the sheep," said the shepherd. He watched the young man select one of the animals and bundle it into his car.

Then the shepherd said, "If I can tell you exactly what your business is, will you give back my sheep?"

"OK, why not," answered the young man.

"Clearly you are a Six Sigma Black Belt," said the shepherd.

"That's correct," said the yuppie, "but how did you guess that?"

"No guessing required," answered the shepherd. "You turned up here although nobody called you. You want to get paid for an answer I already knew, to a question I never asked, and you don't know crap about my business. NOW, give back my dog."

-- author unknown, collected from an e-mail forward (2003)

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