Standard Deviation

In the previous article, we discussed on What is Six Sigma and its main four elements. This article will discuss the significant statistical concept we use in Six Sigma, the standard deviation.

What is Standard Deviation?

The driving goal of Six Sigma is to reduce defects. By reducing defects, teams can increase productivity, decrease overall costs, increase customer satisfaction, and create maximum profit. One idea inherent in the Six Sigma methodology is that variance is the root of many defects.

For example, if an oven heats to precisely 150 degrees in five minutes and stays at that temperature until it is turned off, it is less likely to burn cookies. If a cook measures each ingredient precisely, they are more likely to turn out cookies that consistently taste good. Add variation in the process, and consistency is lost. When consistency is lost, defects are introduced. If the oven doesn’t maintain an exact temperature all the time, the cookies might burn. If the cook puts in a cup of sugar instead of a cup and a half, the cookies might not be sweet enough.

Variation makes for inconsistent quality. It’s important to note that removing variation alone doesn’t constantly improve quality. What if the cook set the oven to 200 degrees all the time and only used half a cup of sugar for each batch? The process has no variation, and neither do the results. The cookies will always be bland and burnt.

Six Sigma process improvement teams usually take a two-step approach to improvements. First, they have to determine if the process is functional. In the cookie example, does the recipe work at all? Is there even a recipe? Once the team chooses a workable recipe, they make improvements to remove the variation that causes outputs to deviate from the result intended by the recipe.

The statistical measure used by teams to understand variation in a process is the standard deviation—the lower case Greek letter Sigma (σ).

Standard deviation measures the distance between data points and the mean of all data. A large standard deviation means an overall wide spread of points; a smaller standard deviation indicates a closely clustered set of points

Standard Deviation in Six Sigma

The image above provides a graphical representation of deviation. Imagine the vertical axis is a measure of time, and the horizontal axis is a measure of temperature. The centerline in each image represents the mean temperature. You can see that the temperature over time varies much more in the figure on the night Calculating Standard Deviation for Population Data

Why Calculating Standard Deviation

Standard deviation in six sigma gives you an idea of how much variation exists in a process while considering outliers. For example, the sample standard deviation indicates that most of the grades will fall within 10.33 points on either side of the average. That tells the teacher that students have a reasonably wide performance on test.

If the results were an average score of 90 with a standard deviation of 3, the teacher might assume that students in the class were learning and retaining the knowledge as expected.

If the average score was 64 with a standard deviation of 2, then the teacher might assume students in the class were not retaining the knowledge as expected, or there was some issue with the test structure.

These situations indicate a small variance in the way students are performing, which points to the success or problem being tied to the class, the teaching, or the test.

On the other hand, if the average score was 60 with a standard deviation of 30, some students were performing very well while others were performing poorly. This scenario might indicate to the teacher that some students are falling behind. Suppose the teacher took samples from several classes. In that case, the teacher might investigate and realize that the lowest scores were mostly from one class, indicating that the teacher forgot to cover a certain concept in that class adequately.

Standard deviation alone serves as a pointer for where to investigate within the process for problems or solutions. But it is not the only indicator to show the process is good or bad. Another reason to calculate it is that it is involved in many of the other statistical methods we cover in Six Sigma. Standard deviation becomes an essential concept in analysis and statistical process control and often serves as the starting point for further Statistical Six Sigma analysis.