Six Sigma
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Last Word
John Guaspari

It Just Doesn't Add Up

And they say numbers don't lie…

The "Jeopardy!" answer was, "By his or her 18th birthday, the average American will have viewed 40,000 of these." The "Jeopardy!" question? "What are murders?"

 When I heard this statistic, my first thought was, "The average American ought to move to a better neighborhood." Then I realized that the category was "Television," and they were talking about murders seen on TV shows. So I relaxed, because the "Jeopardy!" answer wasn't quite so gory after all--it was just nonsense.

 Do the math. It works out to a little more than six murders per day. Are we really supposed to believe that for the first 18 years of their lives, Americans see more than 40 murders on TV every single week? What are these people watching? The Manson Channel?

 Here's a likelier explanation. The number 40,000 is, to use the technical, statistical term, "wrong." But it's big, so people don't question it, which brings us to Guaspari's Immutable Law of Mathematical Obfuscation No. 1: The more zeroes a number has, the more likely people will be to accept it at face value. This law explains why a national debt of several sesquiheptilian dollars is not a problem, but men will shave before stepping on the scale in the morning in order to save a gazillionth of an ounce. (What? I'm the only one who does this?)

 You run into this stuff all the time. I remember an example W. Edwards Deming often used during his legendary public seminars. He would project a slide of an actual newspaper headline that read: "Survey Shows that Half of U.S. Presidents Rated 'Below Average.' " Then he would add dismissively, "Why does this qualify as news?"

 Another more lurid example demonstrates how deeply entrenched this sort of sloppy thinking is in our popular culture. Harold Robbins, the author of 22 cheesy sex-and-drug-filled novels, died last year. I remember reading several obituaries, each of which stated that Robbins' books sold more than 750 million copies, which is pretty doubtful on the face of it. All doubt is removed when the same obituaries went on to say that his most popular novel, The Carpetbaggers, sold 6 million copies. So his most popular book sold 6 million copies… and the other 21 sold, on average, 35 million copies each. Which brings us to Guaspari's Immutable Law of Mathematical Obfuscation No. 1a: People will be less picky about the numbers if they are distracted by repeated references to "heaving bosoms" and "creamy thighs."

 What we're talking about here is "innumeracy," a concept popularized in mathematician John Allen Poulos' 1990 book, Innumeracy: Mathematical Illiteracy and Its Consequences. Poulos argues that because a shockingly large number of Americans simply haven't got a good sense of or feel for numbers, they tend to accept numbers and statistics uncritically, even if these figures represent patent nonsense.

 Why is innumeracy important? Because it affects important things, like baseball. When was the last time the manager of your favorite team justified sending up a pinch hitter who was batting just .211 on the grounds that "the law of averages" was on his side? By that logic, when you go in for your bypass operation, you shouldn't go with a surgeon who has an unblemished record of success. You should pick one who's been losing patients left and right, because he'd be about due to get one right.

 Innumeracy can affect quality initiatives, too. What I have in mind here is some of the current enthusiasm around the whole notion of "six sigma." Please understand that yes, I think it is a good thing that organizations aspire to ambitious quality goals, and yes, I think that striving to perform at a level of just 3.4 defects per million opportunities qualifies as "ambitious." My concern is that even a fairly slight degree of innumeracy can lead to an imprecise understanding of the six sigma concept, which in turn can lead to a line of reasoning that goes something like this:

 "Performing at a six sigma level means creating just 3.4 defects per million opportunities for defects to occur. Well, a defect can occur at any instant in time, and, theoretically, there are an infinite number of such instants in any given second in time. But we should hold ourselves to a tougher standard than that. Let's divide each second into only a million instants. Let's see… that means that if we can go one-third of a second without creating a defect, we're performing at a six sigma level!"

 Do you see the problem? On the other hand, I can make the case that we're lucky that six sigma is as tough as it is. My theory developed as follows:

 1. The first six sigma effort was launched when somebody in management someplace decided, "We need to put more 'oomph' into our quality program."

 2. Such programs, of course, have to have a catchy name. Sigma, as we know, stands for "standard deviation." "One Sigma!" doesn't have much pizzazz. Neither does "Two Sigma!" or "Three Sigma!" or four, or five, or… "Six Sigma! That's it! That sounds like a slogan!"

 3. Once management checked with the people in quality management and discovered that six sigma meant about "one defect every 300,000 opportunities," the decision was made. (See Guaspari's Immutable Law of Mathematical Obfuscation No. 1.)


 But imagine now a slightly different scenario. What if, instead of "standard deviation," the person who first labeled the concept had called it the "theoretical spread"? That would have been a plausible name for it, right? OK, stick with me now, because this is really quite brilliant:

  If it had been called the "theoretical spread," which Greek letter would have been used? That's right. Theta, not sigma.

  If theta had been used, which slogan would have emerged? "One Theta!"? No. "Two Theta!"? No. "Three Theta!"? Yes! That's it! Three Theta!

  A quick call to the folks in quality management, and the standard would have been set. Not 3.4 defects per million, but more than 66,000 defects per million!


 You're questioning the validity of this reasoning? What if I told you that such a goal was almost 20,000 times less rigorous than the one provided by six sigma? That it would lower quality standards by fully 2,000,000 percent?

 Pretty convincing, no? But that shouldn't come as a surprise. After all, Guaspari's Immutable Law of Mathematical Obfuscation No. 1 is a pretty powerful thing.

About the author

 John Guaspari is co-founder of Guaspari & Salz Inc., a management consulting firm based in Concord, Massachusetts. His newest book, The Value Effect: A Murder Mystery about the Compulsive Pursuit of "The Next Big Thing," will be published by Berrett-Koehler in July. E-mail him at jguaspari@qualitydigest.com .

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