## Key Points

- Process shifts are naturally occurring within any process.
- Process shifts are calculated over months, not years.
- Understanding how the shifts occur can help you hone in on inefficiencies found in any process.

What does a 1.5 Sigma Process Shift signify?

iSixSigma released a Process Sigma Calculator. It allows the operator to input process opportunities and defects and easily calculate the Process Sigma. It determines how close (or far) a process is from 6 Sigma.

One of the caveats written in the fine print refers to the calculator using a default process shift of 1.5 Sigma. From an earlier poll, greater than 50 percent of polled quality professionals indicated that they are not aware of why a process may shift 1.5 Sigma. My goal is to explain it here.

## Explaining the Process Shift

I am not going to bore you with the hard-core statistics. Every Green, Black, and Master Black Belt learns the calculation process in class. If you did not go to class (or you forgot!), the table of the standard normal distribution calculates the Process Sigma.

Most of these tables, however, end at a z value of about 3. In 1992, Motorola published a book (see chapter 6) entitled *Six Sigma Producibility Analysis and Process Characterization*, written by Mikel J. Harry and J. Ronald Lawson. It is one of the only tables showing the standard normal distribution table out to a z value of 6.

Using this table you’ll find that 6 Sigma actually translates to about 2 defects per **billion** opportunities, and 3.4 defects per **million** opportunities, which we normally define as 6 sigma, really corresponds to a sigma value of 4.5.

### Tracing the Process Shift’s Origin

Where does this 1.5 Sigma difference come from? Motorola has determined, through years of process and data collection, that processes vary and drift over time. They call this the Long-Term Dynamic Mean Variation. This variation typically falls between 1.4 and 1.6.

After a process has been improved using the Six Sigma DMAIC methodology, we calculate the process standard deviation and sigma value. These are considered to be short-term values because the data only contains common cause variation. DMAIC projects and the associated collection of process data occur over months, rather than years.

Long-term data, on the other hand, contains common cause variation and special (or assignable) cause variation. Short-term data does not contain this special cause variation. It will typically be of a higher process capability than long-term data. This difference is the 1.5 sigma shift. Given adequate process data, you can determine the factor most appropriate for your process.

## Why It Matters

Changes are going to happen throughout any process. Think about it, if you’re working at any scale there are bound to be variations. This can come from changes in suppliers, shifting customer needs, and so forth. Being able to account for these issues

## Accounting for Errors

In *Six Sigma, The Breakthrough Management Strategy Revolutionizing The World’s Top Corporations*, Harry and Schroeder write:

“By offsetting normal distribution by a 1.5 standard deviation on either side, the adjustment takes into account what happens to every process over many cycles of manufacturingâ€¦ Simply put, accommodating shift and drift is our ‘fudge factor,’ or a way to allow for unexpected errors or movement over time. Using 1.5 sigma as a standard deviation gives us a strong advantage in improving quality not only in industrial processes and designs but in commercial processes as well. It allows us to design products and services that are relatively impervious, or ‘robust,’ to natural, unavoidable sources of variation in processes, components, and materials.”

## Other Useful Tools and Concepts

The Sigma Shift is a single component found within DMAIC. As such, if you’re new to DMAIC, it helps to know the other tools at your disposal. We’ve got a comprehensive DMAIC guide that covers the various steps found within this methodology.

Further, understanding how to construct I-P-O models and interpret them is an invaluable skill. These process models act as top-down views of the various ins and outs of your processes and help to get everyone on the same page. You can read all about them in our comprehensive article.

**Statistical Takeaway** for the Sigma Process Shift

The reporting convention of Six Sigma requires the process capability to be reported in short-term sigma â€“ without the presence of special cause variation. Long-term sigma is determined by subtracting 1.5 sigma from our short-term sigma calculation to account for the process shift that is known to occur over time.