## Standard Deviation

**Standard deviation**, represented by the lowercase form of the Greek letter sigma, is a statistic that tells you how tightly the data points are clustered around the mean for a given process, which in turn tells you how much variation exists. When data points are tightly clustered around the mean and the bell-shaped curve is steep, the standard deviation -- and hence the variation -- is small. When the data points are spread apart and the bell-shaped curve is flat, the standard deviation -- and the variation -- is great.

Statisticians generally talk about the number of standard deviations from the mean. One standard deviation in either direction of the mean accounts for 68 percent of the data in the group. Two standard deviations account for 95 percent of it. And three standard deviations account for 99 percent of the data. In Six Sigma, the big question is: How many standard deviations can fit between the mean and the specification limit? We can calculate that number using the formula to the right.

In this formula, Z is the **Z score**, or **Sigma score**. A low Z score means that a significant portion of the tail of the distribution is extending past the specification limit. A high Z score means that not much of the distribution is extending past the specification limit. The table below shows Z scores related to defects per million opportunities. Notice that the Sigma values we identified earlier are represented here.

So, when people in Six Sigma talk about the "sigma of a process," what they're really referring to is the Z score. But the key point is this: You can improve the quality of a process by reducing variation. Your goal is Six Sigma quality, which is an attempt at perfection, or reducing variation to less than four defects per million opportunities measured.

Clearly, Motorola didn't invent the statistics behind Six Sigma. What the company did do is apply the concepts of Gaussian distribution to its manufacturing process with a rigor that had never been seen before. At first, Six Sigma remained an internal initiative at Motorola. But it didn't take long for other companies to hear about Motorola's achievements and to want similar results. In response, Motorola leaders traveled the world teaching Six Sigma to other organizations. Two of the early adopters were Allied Signal and GE. GE did much to popularize Six Sigma, probably because of the results it claimed -- $12 billion in savings in its first five years of use.

In the early years of Six Sigma, the focus was on improving product quality, mostly in manufacturing settings. Soon, however, it became clear that Six Sigma was something more than a way to reduce defects -- it could be used to run the business day-to-day, especially in organizations that truly embraced Six Sigma from top executives down to line workers. Gradually, the definition of Six Sigma also evolved: to achieve a level of quality that satisfies the customer and minimizes supplier losses.

Today, Six Sigma is a business in its own right. Motorola offers Six Sigma consulting and training services through its Motorola University. The company has trained and certified thousands of Six Sigma experts who either work at or consult with organizations all over the world. Motorola is not alone. There are scores of consultants offering a range of Six Sigma-related services, from training and certification to process mapping and implementation.

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