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!