Control Charts

What Are Control Charts

Control Charts were first developed by Walter A. Shewhart during his time at Bell Labs as a graphical method to measure, communicate & control process variation.

In developing this tool, Shewhart recognized that there are 2 types of variation within any process; Normal Process Variation also called Common Cause Variation & Special Cause Variation. Control charts are utilized to clearly distinguish between common variation and special cause variation.

Benefits of a Control Chart

As I said above, the most important benefit of a control chart is that is graphically displays your data in such a way that the special cause variation becomes readily apparent, but there are other additional benefits that Control Charts provide, such as:

They can reduce the QTY of inspection or the need for downstream inspection.
They aid in determining if process improvements are effective.
They set clear “performance boundaries” to aid in process analysis.
They are flexible enough to analyze both variable & attribute data (more on this below).
They Provide a common reference to facility analysis and discussion.

Variation & Control Charts

Shewart knew that every normal process had a certain amount of expected variation, and he also knew that processes occasionally experience Special Cause Variation.

He needed a method to separate these two types of variation and using by a Control Chart he was able to graphically display this data in such a way that the Special Cause Variation became very easy to identify.

This original concept of a control chart has now become a basis for the concept of Statistical Process Control.

Normal Distribution

Control Charts often depend on process to be “Normal”. This means that the process output, or whatever is being measured, is normally distributed.

As you may already know about Normal Distributions, they can be fully characterized by two features, their mean and their standard deviation.

For some control charts, instead of the standard deviation, your control limits will be based on the range of the data. This is normally when the sample size of your subgroup is between 1 to 10 samples.

Elements of a Control Chart

Similar to Normal Distributions, Control Charts rely heavily on the process output mean and the process output standard deviation (or range) to determine if a process is in-control or out of control. The most important element of a control chart is the Mean. This is the average expected value for a process output.

The 2nd most important element of a control chart is the Control Limits. Every Control Chart has an Upper Control Limit (UCL) and a Lower Control Limit (UCL). These limits are used to determine if a process is in-control or out-of control. So, A process is considered in-control if all the data points collected fall within the Control Limits of a Control Chart (more on trending below).

The last major element of your control chart are your axes. The X-Axis for most Control Chart represent things like units, subgroups or time. The Y-Axis of your control chart represents the value you’re measuring.

Data & Your Control Chart

Once you’ve defined all the major elements of your control chart, the next step is deciding what type of data you plan on collecting & analyzing. There are 2 major types of Quantitative data; continuous (variable) data & discrete (attribute) data.

Discrete data is things like Pass/Fail, Yes/No, Percentages (scrap rate), or counting occurrences of data.
Continuous data represents any measurement on a continuous scale. Examples might include Temperature, Length, Dosage, Tensile Strength, Leak Rate, etc.

Sample Size & Sub-grouping

The next data element to consider is sample size & sub-grouping. The data points on your control chart can be individual data points or they can be the average of a sample of data, this is an important concept in Control Charts called Sub-Grouping.

For example, let’s say you build 10 discrete lots of a certain product every day where each lot has 100 units of product. From each of those 10 lots, you pull 5 samples to destructively test. Those 5 samples are considered your sub-group. The sample size of this subgroup is 5 and is important to note as it will assist you in selecting the right control chart.

[table id=3 /]

Then from this data you can calculate the Lot Average (X-Bar) and the Lot Range (R).

[table id=4 /]

We can also use this data to calculate the Grand Average (1.2612) and the Grand Range (0.40) of the entire data set which is used to create our control limits. More on this below.

Selecting the Right Control Chart

It is very important that you select the correct control chart! Selecting the incorrect control chart might lead you to incorrectly analyze your data, miss special cause variation or take action on variation that you think is special cause when it’s actually common cause.

As you may have seen, Control Charts are also commonly paired together. For example, the X-Bar R (Range) Chart pairs together a control chart for X-Bar (Average) with a control chart for the Range (R) of the data. This pairing allows you to study the variation between data points (X-Bar graph) AND the variation within a subgroup (range graph).

There are many different control charts which have been created to properly analyze different data types. For example, there are different charts between continuous data and discrete data. There are also different control charts depending on the sample size of the subgroup that you’re measuring.

If you’re sub-grouping, it’s important to remember that the Grand Average, Grand Range & Grand Standard Deviation is just the Average, Range & Standard Deviation of the entire population of data that you’ve measured.

Note: These values should only be calculated from the process when it is considered “in control”. I’ve put together a step-by-step guide to go along with the flowchart below to help you select the right Control Chart.

Determine the type of data you’re collecting (Continuous v. Discrete)

For Continuous Data:

Determine the sample size of your subgroup

For Subgroup Size N = 1, use the Individual & Moving Range Chart

For Subgroup Size 2 < N < 10 , use the Xbar – R (Range) Chart

For Subgroup Size N > 10, use the Xbar – S (Standard Deviation) Chart

For Discrete Data:

In the situation where multiple defects can occur on any given unit or sample, choose a C-chart or U-Chart based on the consistency of the sample size. In the situation where only 1 defect can occur on any given unit or sample, choose an NP-chart or P-Chart based on the consistency of the sample size. See the chart above for guidance.

Setting Limits & Trending

Before you’re able to accurately set the limits on your control chart, it’s important to collect data from the process for a time period, or a defined number of samples where you believe the process is in control. Additionally, the limits on your control chart depend on the type of control chart that you need to use.

The most common limits used on control charts is 3 times the standard deviation. For more information on setting limits on your control chart, I highly recommend checking out this post on iSixSigma.

Trending Rules

In determining whether your process is in control or not there are a number of rules that have been developed to detect a trend. These trend rules are what indicate that special cause variation is effecting the process. It are these special causes that must be eliminated from your process.

Rule 1: Any 1 point outside a 3-sigma limit.
Rule 2: 2 out of 3 successive points on the same side of the centerline that are 2-sigma from the average (centerline).
Rule 3: 4 out of 5 successive points on the same side of the centerline that are 1-sigma away from the average (centerline).
Rule 4: 8 Successive values on the same side of the centerline regardless of their distance from the centerline (average).

Limitations & Downsides of Control Charts

Control Charts can be used incorrect if an incorrect sample group or process parameter/output are chosen. For example if a non-homogeneous sample is chosen, then the results will be skewed.
Incorrect decisions can be made without understanding of the variation (error) associated with your measurement system.
Control charts are often incorrectly used to determine your process capability, however this is incorrect. Control charts can only communicate the current process performance.

Control Chart Definitions

[table id=2 /]

Relevant Videos:

Here’s a quick explainer video about control charts from Keith Bower.

Here’s another quick video that explains some of the same concepts we discussed above.

You can check out more CQE related videos on my YouTube Channel.

External Links:

I wanted to include some links to some other good, free online resources for Control charts.

Other Cool Stuff

Wanna do me a favor? I’ve created a quick, 3 minute survey to get your feedback! CQE Academy Survey <- Thanks!!!

Want to continue learning? Continuous Improvement, Product and Process Control, Product & Process Design.

Have General questions about the CQE Exam, check out my FAQ.

Want to learn more about me or CQE Academy, check the About Me page.

Thanks,

Andy