Sigma is the eighteenth letter of the Greek alphabet, and in statistics, it stands for the standard deviation. Standard deviation is a measure that is used to quantify the amount of variation or distribution of a set of data values.

Statistics were first applied to quality control in business by Walter Shewhart, an American engineer, physicist and statistician. His work formed the foundation of modern Six Sigma programs, a set of techniques and tools for process improvement. Lesser known than the concept of Six Sigma is that of Three Sigma.

How to Use This Measurement

Calculating sigma or the Standard Deviation helps to answer a question that arises with virtually every major new finding in science or medicine: What makes a result reliable enough to be taken seriously? When determining statistical significance, the standard deviation is used. Deviation shows how far a given data point is from the average.

Often, the results of an experiment follow what is called a “normal distribution.” For example, if you flip a coin 100 times and count how many times it comes up heads, the average result will be 50. However, try this test 100 times, and most of the results will be close to 50, but not exactly. Testing the coin with 100 flips will result in as many cases with 49 or 51. Also, you're likely to get quite a few 45s or 55s but almost no 20s or 80s. Plotting your 100 tests on a graph will result in a bell curve, a well-known shape that is highest in the middle and tapers off on either side, which is considered a normal distribution.

3 Sigma Example

In the coin example, a result of 47 has a deviation of three from the average of 50 or 3 standard deviations from the norm. One sigma or one standard deviation plotted above or below the average value on that normal distribution curve would define a region that includes 68 percent of all the data points. Two sigmas above or below would include about 95 percent of the data. Three sigmas would include 99.7 percent.

R Chart Use

In statistical quality control charts – sometimes called an r chart – three-sigma limits are used to set the upper and lower control limits. R charts are used to establish limits for a manufacturing or business process and are based on the theory that a certain amount of variability in output is inherent, no matter how perfect the process. Control or r charts can help determine if there is a controlled or uncontrolled variation in a process. Variations in process quality due to random causes are said to be in-control. On the other hand, out-of-control processes include both random and special causes of variation. An r chart is used to determine the presence of special causes.

Enter Motorola and Six Sigma

As a measurement standard, Six Sigma traces back to the 1920s and Walter Shewhart. He showed that three sigma from the mean is the point where a process requires correction. Many measurement standards arrived after Shewhart, but a Motorola engineer named Bill Smith coined the term Six Sigma.

In the early- and mid-1980s, Motorola engineers decided that the traditional quality levels weren't precise enough for the modern era. Per thousand measurements weren't cutting it. They wanted to measure the defects per million opportunities. Motorola developed this new standard which they called Six Sigma. The company also created the methodology and cultural change associated with looking so closely at errors and perfection. Six Sigma helped Motorola improve their processes so much that they documented more than $16 billion in savings as a result of Six Sigma efforts.

Today, thousands of companies around the world use the Six Sigma method as a way of doing business.

Why Six Sigma?

Motorola changed the discussion of quality from one measuring in percent – parts-per-hundred – to a discussion of parts-per-million or even parts-per-billion. The company decided that modern technology was so complex that old ideas about acceptable quality levels no longer worked. The idea was that modern businesses require much stricter quality levels.

The old three sigma quality standard of 99.73 percent translates to 2,700 parts per million failures. Three sigma was out, and six sigma was in.

Six Steps of Six Sigma

Six Sigma has evolved from more than a theory or “training." It has created an entire business culture based on precise process improvement. Many companies have a proven track record of saving large amounts of money by applying Six Sigma to the organization's business processes. In 1999, for example, GE Capital purportedly saved $2 billion with Six Sigma.

The Six Sigma process is broken down into six steps: Define, Measure, Analyze, Improve, Control and Synergize.

Define: First, the issue or problematic process must be well-defined in tangible, quantifiable terms with a working description. A group dedicated to the Six Sigma assignment will select a project by choosing options that reflect the organizational goals. This is accomplished during the Define phase, and the result is a map of the process that will be improved.

Measure: This is when the process is clearly outlined and scrutinized to define the process steps. Having correct metrics is an important part of this phase. To that end, it is essential that any metrics be validated as reliable during this phase. This way, the project's process can be accurately monitored.

Analyze: In this phase, the reasons for errors that need to be corrected will be assessed and analyzed. The Analyze phase is also key to providing insight as to how the company can close the gap between the current level of performance and the anticipated level.

Improve: This is a challenging but rewarding phase of the Six Sigma process. During the Analyze phase, problems are detected and laid out. During the Improve phase, the group can determine innovative solutions.

Control: If the correct change management strategies were identified in the previous stages, then the control phase should be successful. At this point, the group will create a formula for handing off the process. This will include procedures and information to ensure success moving forward.

Synergize: This step is key to success. During Synergize, the team in charge of the Six Sigma operation makes sure its plans and solutions are shared with the organization as a whole. This sharing is necessary to change the company's culture and create a learning organization.

The Future of Process Improvement

While three sigma worked well for a very long time, the Six Sigma process and its higher level of improvement is necessary for the modern era. The requirement of extremely high quality is essential to so many modern day processes. Quality Control Inc., a software company focused on process improvement, crunched some numbers to find out all the ways that three sigma quality could negatively affect certain processes. The company asserted that if three sigma was applied, the results could be devastating:

  • 10.8 million health care claims would be mishandled each year.
  • 18,900 U.S. savings bonds would be lost every month.
  • 54,000 checks would be lost each night by a single large bank.
  • 4,050 invoices would be sent out incorrectly each month by a modest-sized telecommunications company.
  • 540,000 erroneous call details would be recorded each day from a regional telecommunications company.
  • 270 million erroneous credit card transactions would be recorded each year in the U.S.

The modern world demands very high levels of performance. Six Sigma arose in response to this, and it is a necessary tool for modern businesses.