Six Problems I have with Six Sigma, Part I
by David C. Crosby
November 23, 2009

Source: http://bit.ly/amd9zv

Problem one, The Concept

I see Six Sigma as a performance standard-which is 3.4 defects per million opportunities (DPMO). I guess it means that 3.4 defect/million is okay-or maybe not. Sigma, of course, is a unit of distance of individuals from the average of a population. However, I don’t see where Six Sigma has much to do with sigma. This is my first problem with Six Sigma. Very few people understand sigma-standard deviation-or can calculate it, or even care. So, Six Sigma must be translated into everyday language: 3.4 defects per million operations, or DPMO as they say. I’m not sure what four tenth of a defect is, but that’s okay.

How does one calculate sigma? One Six Sigma book I read used a kind of conversion table showing % yield and sigma values in two columns. If you follow the yield column until you reach 99.99966%, that’s 3.4 DPMO, or 6 sigma. That’s probably why a black belt once told me that it was simple to calculate sigma; you simply multiply by 3.4. Really? She wasn’t clear about what to multiply by what.

As any quality professional can tell you, there is sigma and there is sigma. It looks to me like sigma used in Six Sigma is only an estimate of standard deviation; sometimes called sigma hat. In case you don’t know-in a process capability study-sigma is calculated by dividing the average range of the samples by a constant value (d2), which taken from a statistical table. So, it’s an estimate because the individuals measured are just samples of the process. Every characteristic of every part could have a different average range, thus a different sigma. If you make thousands of parts with thousands of characteristics, you would have that many sigma values. Which sigma value is used for Six Sigma? To complicate things, the d2 value changes with the sample size, which means that sigma will also change if the sample size changes.

A process capability study is just a statistical guess of the chances that a variable might exceed its specification. It’s a calculated guess, not an absolute.

You can only calculate the true sigma when you have measured the entire population. Of course, then the work is done-the game is over-and what you have is what you have. So, that sigma is only usable as history or for analysis. Instead of calling it Six Sigma, you could and just make up a word and say it means 3.4 DPMO. “Depmo” sounds good. Another thing. Every statistical text book I’ve ever read, uses the word about when discussing sigma-the distribution of individuals under a normal curve. Unlike the table in the Six Sigma book, they say about 68% of the individuals will be within +/- one sigma away from the average. Not exactly 68%, but about 68%. About 99.7% will be within +/- three sigma and so on. In theory if you got out to +&- six sigma, you might get a number of about 3.4, or you could get more, or you might get nothing.

The Six Sigma method may be an effective tool for solving process problems and getting corrective action, that’s wonderful. But why the sigma nonsense? Quality Engineers have been doing that since the year one. Anyway, if you can reach 3.4 DPMO, why not just go ahead to Zero DPMO, or Zero Defects?