# Control Limits are the Key to Control Charts

## Control Limits are Used to Determine if a Process is Stable

Control limits are the "key ingredient" that distinguish control charts from a simple line graph or run chart.
Control limits are calculated from your data. They are often confused with specification limits which are provided by your customer.

### Control Limits on a Control Chart

• Control limit calculations begin with the Center Line (the average or median of the data.)
• Next calculate sigma. The formula for sigma depends on the type of data.
• From the center line, lines are drawn at ± 1 sigma, ± 2 sigma and ± 3 sigma.

+ 3 sigma = Upper Control Limit (UCL)
- 3 sigma = Lower Control Limit (LCL)

### How are Control Limits Calculated?

The hard answer: The formula for sigma depends on the type of data you have. Is it continuous or discrete? What is the sample size? Is the sample size constant?

In short, each type of data has its own distinct formula for control limits and, therefore, is a different type of control chart. There are seven main types of control charts (c, p, u, np, individual moving range XmR, XbarR and XandS.) Plus there are many more variations for special circumstances. As you might guess, this can get ugly. Here are some examples.

p chart formula

Individual Moving Range chart formula

X bar R chart formula

### You Can Try and Calculate Control Limits Yourself, But ...

• It will suck up a bunch of your time.
• You'll probably make mistakes and aggravate customers.
• And you will find your homegrown template hard to maintain.

Based on calls to our tech support line, most people who try to perform manual calculations or build their own Excel formulas end up with incorrect results.

QI Macros is an easy to use add-in for Excel that installs a new tab on Excel's toolbar.

QI Macros calculations are tested and accurate and it will highlight unstable points and trends in red.

Even better, QI Macros control chart wizard contains code that will select the right chart and formulas for you!

### How Many Data Points are Used to Calculate Control Chart Limits?

Generally, you calculate control limits using your first 20 to 25 data points and then you use those limits to evaluate the rest of your data. If you have a process change, you should recalculate your control limits beginning with data after the process change occurred.

When you select data and then run a control chart using QI Macros, QI Macros will use ALL of the data points selected to calculate the center line (ie. average). If you have 14 points it will use 14 points, if you have 26 points it will use 26 points, etc.

The center line is then used to calculate the 1 and 2 sigma lines and the upper control limit and lower control limit.

To check which points are used to calculate your center line, simply move the chart to reveal the calculations behind it. Click on the first cell under the cell labeled "Average". You can determine the data range used by viewing the formula in Excel's formula bar.

In the following example, we clicked on cell H2 and noted that the average is calculated using cells B2 to B26 and C2 to C26.

### QI Macros Makes it Easy to Update Control Limit Calculations

Once you create a control chart using QI Macros, you can easily update the control limits using the QI Macros Chart Tools menu. To access the menu, you must be on a chart or on a chart embedded in a worksheet.

#### Here's what you can do with the click of a button:

There are also options to easily re-run stability analysis after changing data or control limit calculations.

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• Works right in Excel
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