I recently got into a great discussion on LinkedIn and before replying to a post I wanted to clarify my thoughts. Well, 1300 words later and a lot of digging around on forums and this is what I discovered. Hope this helps bring clarity on practical uses of Control Charts – it was a fun Sunday morning exercise!

## Why should you use Control Charts to Map your Process?

Charting the process will give you the tools to verify the performance – see if a process is under statistical control. It also helps you monitor the effects of improvement efforts.

## Why do you want your Process to be under Statistical Control?

Once you reach an acceptable level of stability, you can feel confident that the process will perform in a consistent manner. It is meaningless to say that the process IS 4.5 sigma if its behavior IS NOT consistent over the time or unstable.

Also, once a Process is under statistical control, you can begin to apply some of the other tools to improve performance. Trying to improve performance before a process is under control can actually make things worse. See the Quincunx demonstration for a great visual on this.

## Why you would want Control Limits less than 3 Sigma?

The aim of control charts is to reflect process stability, or equivalent behavior over time. Given a normal distribution 99.73-something % of your distribution would lay inside 6 standard deviations or sigmas. On a control chart, half would be above and half below. Thus, positive 3 sigmas for the UCL – Upper Control Limit and negative 3 sigmas for the Lower Control Limit.

The name of the game here is to use control limits to decide not only if something is broken in your process, but if it is a special event or a common event – because that dictates your next actions. (See below).

A point outside of that 6 sigma band – above the UCL or below the LCL means that the process is out of control. The reasoning is that it is so unlikely that a point would be delivered by the process behaving as usual that you could reasonable suspect that the process is no longer under control.

If you use control limits at too few sigmas you are reducing the percent likelihood that a point will land in the band. Thus, any small shift in the process behavior will be detected but you will also have too many points outside the limits **just by chance** when there is no special cause to address giving you many false alarms.

If you use control limits at too many sigmas, you are increasing the chances of a point landing in the bands. Virtually the whole population will fall within the limits and then there will be no false alarms but you’ll miss most shifts in the process. That leads to missed opportunities for improvement – in which case, why are you charting the process in fist place?

The key here is cost/risk management. We are trying to find the economic trade off between the act of charting the process and investigating vs the cost of missing an instance of variation that would cause financial issues – the cost of poor quality. Control limits at 3 sigmas were found (and are widely accepted) to be a good balance.

Control limits are based on historical data and process variation. As your process capability improves the control limits will need to be recalculated.

## When Should I Recalculate my Control Limits?

The short answer is once the control charts cease to have meaningful business applications. This could be either that you have improved or altered the original practice so much that you have, in effect, a new and different process than what you started with.

What does this look like in practice? After your process has reached a point of statistical control you should have a good history of data. Then you can begin using trend analysis.

Basic trend analysis:

- Lack of plotted points near the control limits
- Points avoiding the outer zones, and various other out of control conditions.

As a result of the reduced variation in your process, the new sigma is less than the original sigma. That is, the spread of the new +/- 3 sigma limits will be less than the previous limits.

## Can Control Charts tell me the Sigma Level of my Process?

Control charts do NOT measure the sigma level of an overall process. They measure whether a process is in statistical control, ie: does the process generally follow a normal distribution.

“3 sigma control limits” refers to stability – or equality of behavior over the time. “Operating at n sigma” refers to performance.

Since +/- 3 sigma encapsulates 99.73% of the data in a normal distribution, if you process falls within that limit, you have a process that is in statistical control.

The sigma calculation is used to measure the performance or effectiveness of the project on the end results of the process. The six sigma philosophy is a methodology for continuous improvement. Achieving 6 sigma (3.4 Defects per Million) was set because that was the acceptable level of cost of poor quality – anything less and the business isn’t viable or is grossly impacted. Today, many industries aim for much stricter quality standards again driven by business.

Performance is how fit is your process to meet the specifications. Note that “specification” is not used in control charts, because it has nothing to do with stability. A process operating at 6 sigma means that the process average is 3 sigmas away from the closest specification limit – 3 from the UCL and 3 from the LCL. Thus, virtually no output is out of specification.

Another way to look at this is that the process is what it is regardless of whether you chart it or not, what your control limits are, or what your graph looks like. Changing the control limits do not change your process performance, and hence do not change the “sigmas” at which your process operates.

The control chart and sigma calculations are separate measurements, and should always be treated as such.

## What do you do if a Point falls outside the Control Limits? Ex Above the Upper Control Limit or Below the Lower Control Limit?

This depends on the history of your process.

If you are just getting started and there are points outside the limits, you must get your process under control first. Lower the center and spread of your process values by eliminating or reducing variation.

If a process was under statistical control and then you find a **single** point outside of the there is a special cause of variation. First be sure this is a special, one-time-only variation. Then try to set controls in place to eliminate or prevent it coming back. Using a prioritization tool like FMEA helps. Note that if you end up changing your standardized process to account for the special cause variation, you’ll need to re-calculate your control limits as you now have a new process in place.

If you find multiple points outside the control limits, there is probably common cause variation. This is when you should apply six sigma methodologies like DMAIC to reduce the variation in your process.

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