## Six Sigma

Read this chapter, which gives a clear description of Six Sigma, when it is used, and how to interpret the results.

### Introduction

Every generation of business strives for a new level of quality. The quality program that is currently in vogue and being widely used and recognized by industry is the Six Sigma program. Six Sigma is a relatively new program, and was only started in 1986. It was first put into implementation at Motorola, but is now in use by most large corporations. Some of these other large companies include GE, Honeywell, and Bank of America. The Six Sigma program is in place to eliminate any abnormalities, failures, or defects that occur within a given process. These are problems that already exist. DFSS (Design for six sigma) starts earlier, to develop or redesign the process itself, so fewer wrinkles show up in the first place, thus systematically preventing downstream errors. Six Sigma is also used in developing new processes. The Six Sigma program strives to achieve six standard deviations between the mean and the closest specification limit on a short term study. Studies run to obtain this goal are short term capability studies, which include common cause or random variation, such as operator control, and long term studies, which include random and special types of variation. Both of these studies are evaluated on a Z-scale. The short term data variability which makes up long term variability tends to cause the mean to shift. This shift of the mean is by 1.5 standard deviations. Most companies are looking on a long term scale, because they would rather have a good/safe product in the long run/for a long time rather than for a short amount of time. Using this idea, the goal for the Six Sigma program is to have fewer than 3.4 failures per one million opportunities when the data is evaluated to include the shifted mean from process variability (6 standard deviations - 1.5 standard deviations = 4.5 standard deviations). The 4.5 vs 6 standard deviations is the same goal, but the 4.5 represents data variation in the long run, which is used in most processes. We will be using the shifted mean scenario for the rest of this article when referring to opportunity goals. This leaves very slight room for error on a process and leads to a very high level of quality in the products.

The often-used six sigma symbol.

To reiterate, the term "Six Sigma" comes from the standard deviation and the Gaussian distribution. 3.4 failures per one million opportunities represents 4.5 standard deviations (sigma) away from the median value, either up or down, under a bell curve. This will be discussed further below along with what the Six Sigma program represents, what mathematically this means, and finally what a Gaussian distribution is. After the basics have been covered we will move onto Statistical Process Control. Statistical Process Control is different ways to analyze the data that you have obtained. Finally, we will relate Six Sigma to process control and explain how you can tell if something is in Six Sigma control or not.

Source: Peter Woolf et al., https://eng.libretexts.org/Bookshelves/Industrial_and_Systems_Engineering/Book%3A_Chemical_Process_Dynamics_and_Controls_(Woolf)/13%3A_Statistics_and_Probability_Background/13.03%3A_Six_Sigma-_What_is_it_and_what_does_it_mean%3F

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