Control charts are one of the hardest things for those studying six sigma to understand. Here’s an easy Control Charts Study Guide for you. When I was studying for the Six Sigma Black Belt Exam I noticed there were a lot of questions on control charts. Besides that, I noticed that there were a lot of different types of control charts. You had to use one for certain kinds of data or number of units in the sample and then you had to use other control charts in different instances.

Beyond that, different distribution types associated with several of the data sets. Something you take for granted when asked a question specifically geared to data, but I found it was easy to get tripped up on the exam when combining with control chart questions.

Very confusing????

So, in the spirit of continuous improvement, we made the following control charts study guide.

Control Charts Study Guide Overview

Control charts : A Control chart is one of the primary techniques of statistical process control (SPC). The control chart is a graphical display of quality characteristics that have been measured or computed from a sample versus the sample number or time. The control chart was invented by Walter Shewhart at Bell labs in 1920.

Statistical Process Control – Statistical Process Control (SPC) is a statistical method to measure, monitor, and control a process. In other words, SPC is a method of quality control which employs statistical methods to measure, monitor, and control a process.

Common Cause: A cause of variation in the process is due to chance, but not assignable to any factor. It is the variation that is inherent in the process. Process under the influence of common cause will always be stable and predictable.

Assignable Cause(“special cause”): The variation in a process that is not due to chance, therefore, can be identified and eliminated. Process under influence of special cause will not be stable and predictable.

Rational Sub Grouping: Rational sub grouping is the process of organizing the data into groups which were produced basically under the same conditions. Rational subgroups help in the estimation process of the short term variations. Thus, rational sub grouping is the basis for operating control charts in a successful manner. These variations later help us predict the long term variations and their control limits, depending o the type of causes for the variation (special or common).

Control Charts by Data Type

The control chart is a graph used to study how process changes over time. A control chart always has a central line for average, an upper line for upper control limit, and lower line for the lower control limit. The control limits are ±3σ from the centerline.

Selection of appropriate control chart is very important in control charts mapping, otherwise ended up with inaccurate control limits for the data. Not all control charts are the same. Different Data Types require different charts.

Control Charts Study Guide

Control Charts for Continuous Data

Measure the output on a continuous scale. It is possible to measure the quality characteristics of a product. Once you know that you are making a control chart for continuous data, you need to determine if your population is normal or not and the sample size (n) you are charting.

No matter what you decide, I think you could start off just making a basic Run chart and seeing where that brings you. It is Just a basic graph that displays data values in a time order. Can be useful for identifying trends or shifts in process but also allows you to test for randomness in the process.

The Data is Normal

Subgroup size n = 1, then use: X-MR or I-MR chart:. An Individual moving range (I-MR ) chart is used when data is continuous and not collected in subgroups. In other words collect the single observation at a time. An I-MR chart provides process variation over time in graphical method. 

If 1 < n < 10, then use X bar-R chart. It is used to monitor the process performance of a continuous data and the data to be collected in subgroups at set time periods. Since n is small, use the range to estimate the process variation. It consists of two plots to monitor the process mean and the process variation over the time.

Else, If n >= 10, then use X bar-S chart. It is often used to examine the process mean and standard deviation over time. Use X bar-S chart when the subgroups have a large sample size and also S chart provides a better understanding of the spread of subgroup data than range.

Special Note: If your data is Not Normal

Note that there is some robust conversation in the industry on this. For your application purposes, I suggest you read the following and make your own decisions (if you’re just studying for certification, you can probably skip):

Control Charts for Discrete / Attribute Data

Attribute control charts are used for attribute data.  In other words, the data that counts the number of defective items or the number of defects per unit. For example number of tubes failed on a shop floor. Unlike variable charts, only one chart is plotted for attributes.

Four types of control charts exist for attribute data. p chart plots the proportion of defective items, and np chart is for the number of defectives. u chart is for the average number of defects per unit and c chart is for the number of defects.

Control Charts Study Guide

When there are Multiple Defects (i.e. chances to be defective): It computes control limits based on the Poisson distribution.

c chart – control chart for defects. It is generally used to monitor the number of defects in constant size units. 

u chart -control chart for defects per unit. It is generally used to monitor the count type of data where the sample size is greater than one. Plot the average number of defects per sample unit.

When there are NOT Multiple Defects:

This population sorts defects into 2 piles (it’s Binomial). Samples are either good or bad, positive or negative, right or wrong.

np chart – control chart for defectives. It is generally used to monitor the number of non-conforming or defective items in the measurement process.

p chart -control chart for proportions. It is generally used to analyze the proportions of non-conforming or defective items in a process.

Control Chart Analysis

The main purpose of control chart is to improve the process. It provides “ Voice of the process” that helps teams to identify special causes of variation in the process. By removing the special cause from the process, process becomes more stable and consistent process.

Out-of-control: A process is “out-of-control,” means special causes exists in either the average chart or range chart, or both. Teams must identify special causes and try to eliminate to achieve a stable process. We can say proces is out-of-control if any point in the control chart is out of control limits or having abnormal patterns of variability.  

Control limits are 3 standard deviations above and below the mean. If the process is in control, 99.73% of the averages will fall inside these limits. The same is true for the range control limits. Because there are two components to every control chart- the average and the range.

Four possible conditions may occur in any process.

Control Charts Study Guide

Average stable, Variation changing (Example)

Five Common Rules for Control Chart Interpretation

Control Chart Rules

Control Charts Study Guide Videos

Other Helpful Articles

I love MoreSteam’s visual that shows the layering of multiple tools here.

Practical Notes on Using Control Charts and Control Limits to Make Process Improvements

Practical Uses and Questions on Control Charts
Practical Uses and Questions on Control Charts. Photo by runran

Here are some Practical Notes on Using Control Charts and Control Limits to Make Process Improvements. 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.

Authors

Comments (9)

YOU ARE A BLESSING! THANK YOU!!!
I’m taking the green belt test next week and the class was an accelerated class (6 weeks)! Ninety percent lecture. I have yet determined a project.

I so agree. This is so concise and perfect for revision. Thank you so much Ted! If I were not married, I would have professed my love for your work 🙂

Hah! I appreciate the note, Swetha. I’m glad it helped. And I’d be remiss if I didn’t share credit with Ramana who contributed heavily to this article – especially the helpful graphics!

Please correct this :
If your data is Not Normal
Use a Run chart.

If your data is “Not” Normal You want to said : Your data is Normal
Thank you

Thanks for bringing this up, Rachid. There were a number of errors on the page that I’ve found and updated thanks to your comment.

Please check out the new section on non-normal control charts and let me know your thoughts.

Hello Ted,

I like your website and I am visiting it from time to time.

Well, I have a small question, I can’t find its answer either in your website or in other books.

Could you help me to answer it?

Select the best option

Question- A percent defective control chart designed for

Option One- Reduce variation of project

Option Two- Identify the cause of variation that lies out the system

Option Three- Ensure that variation of output is due to common causes

Option Four- Detect the existence at special causes of variation

BR,

Icomon

Icom,

Thank you for submitting the question. We have thousands of practice questions and exams available in our membership program where we walk through exactly how to solve each.

We don’t support questions outside our test bank, but this article should direct you to where you need to go to answer this question.

Best, Ted

Icom,

Thank you for submitting the question. We have thousands of practice questions and exams available in our membership program where we walk through exactly how to solve each.

We don’t support questions outside our test bank, but this article should direct you to where you need to go to answer this question.

Best, Ted

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