Six Sigma - What is it?

This may seem totally random, but it's actually related to my posts from a couple of weeks ago about averages.

So, what is Six Sigma? According to Wikipedia:

Six Sigma (6σ) is a set of techniques and tools for process improvement. It was introduced by engineers Bill Smith & Mikel J Harry while working at Motorola in 1986. Jack Welch made it central to his business strategy at General Electric in 1995.

It seeks to improve the quality of the output of a process by identifying and removing the causes of defects and minimizing variability in manufacturing and business processes. It uses a set of quality management methods, mainly empirical, statistical methods, and creates a special infrastructure of people within the organization who are experts in these methods. Each Six Sigma project carried out within an organization follows a defined sequence of steps and has specific value targets, for example: reduce process cycle time, reduce pollution, reduce costs, increase customer satisfaction, and increase profits.

The term Six Sigma (capitalized because it was written that way when registered as a Motorola trademark on December 28, 1993) originated from terminology associated with statistical modeling of manufacturing processes. The maturity of a manufacturing process can be described by a sigma rating indicating its yield or the percentage of defect-free products it creates. A six sigma process is one in which 99.99966% of all opportunities to produce some feature of a part are statistically expected to be free of defects (3.4 defective features per million opportunities). Motorola set a goal of "six sigma" for all of its manufacturing operations, and this goal became a by-word for the management and engineering practices used to achieve it.

Huh? Basically it says that a manufacturing process should have 3.4 defects per million items manufactured. I had to take Six Sigma training with AT&T, but I haven't done anything with it. I think the company has forgotten about it.

I think the number is loosely related to standard deviations in statistics which would be 99.99932% for 4.5 standard deviations, not six. That works out to 6.8 defects per million. I guess the sigma in Six Sigma is not the same as sigma in standard deviations. Six standard deviations would be 99.9999998026825% or 1 defect in 506,797,346!

Let's continue looking at standard deviations. We'll use coin flipping as a simple example.  I think most of us know that if you flip a coin the odds are 50 - 50. 50% of the time we'll get heads and 50% of the time we'll get tails.

If we were to flip a coin 10 times (or flip 10 coins once...which is mathematically equivalent) we would expect about 5 heads (we'll only look at heads now, but the math is the same for tails), not necessarily 5 heads exactly but close. And with 100 coin flips we would expect somewhere around 50 heads. But how close to 50? We can use standard deviations to figure that out. 100 tosses work really well since the standard deviation is exactly five. If we repeatedly flip 100 coins and add up the total heads we would expect the total to be within one standard deviation of 50...or between 45 and 55, 68% of the time. Between 40 and 60 (two standard deviations), 95% of the time. And between 35 and 65 (three standard deviations), 99.7% of the time. That means that if you flipped 100 coins 1,000 times, only 3 times would the total be less than 35 or more than 65. Six standard deviations would be 30, or from 20 to 80. And as we saw above that would only happen 1 in 506,797,346 times! The table I looked at on the Wikipedia page linked to above goes to 7 standard deviations, which would be 1 in 390,682,215,445 times. If you were to flip 100 coins a day, every day, you'd get less that 15 or more than 85 only one time in a billion years!

As a final example, I thought I'd figure out how likely it would be to flip one million heads in a row. If we flip a coin 1,000,000 times we would expect 500,000 heads. The standard deviation in this case is 500. So, 1,000,000 is 1,000 standard deviations from 500,000. If 7 standard deviations only occur once in a billion years, I have no idea when, or if, we'd ever get to 1,000 standard deviations since it's not a straight line but an exponential one.

I think this is it for statistics for awhile. My mind is totally blown at this point!

Interesting days

Today - Saxophone Day, Job Action Day, Broadcast Traffic Professionals Day and Nachos Day

Tomorrow - Bittersweet Chocolate With Almonds Day and Hug A Bear Day

Next Monday - World Kindness Day and World Orphans Day

December 6 -  Pawnbrokers Day, St. Nicholas Day, Put On Your Own Shoes Day, Miners' Day and Mitten Tree Day