Six Sigma

Many of you will have heard of Six Sigma management. What you may not realize is that the etymology of the term Six Sigma is rooted in statistics. As you should have seen by now, statisticians use the Greek letter sigma () to denote a population standard deviation. So, when these Six Sigma people start talking about "six sigma processes," what they mean is that they want to have processes where there are (at least) six standard deviations between the mean and what would be determined to be a failure. For example, you may be examining the output of a factory that makes airline grade aluminum. The average tensile strength of each piece is 65 ksi, and you view a particular output as a failure if the tensile strength is anything less than 64 ksi. If the standard deviation is less than 1/6 ksi, then the process is six sigma. The probability of failure within a Six Sigma process is 3.4 in a million, which corresponds to the 99.9997% confidence level. When we are doing statistics, we usually use the 95% confidence level, which is roughly 2 sigma's. In the case of the tensile strength of airline grade aluminum, 6 sigma is probably a good level to be atcatastrophic failure on an airplane could open you up to lawsuits worth billions of dollars. But there are some other processes that you probably don't need to be so certain about getting acceptable product. Give some examples from your own business life of random processes that are likely to be normally distributed (measured not counted), and say how many sigma's you think the process should be at.