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## Quick reference

### Control Limits

Control limits are the limits of normal common cause variation. Control limits are calculated based upon the data set descriptive statistics. Control limits provide indication of special cause variation.

### When to use

Control Limits are part of an SPC control chart. If creating a control chart you must calculate control limits. If managing or monitoring a process using a SPC control chart, you must use the control limits to watch for special cause variation.

### Instructions

Control limits are an integral part of an SPC control chart. They show the boundaries of normal common cause variation. They are calculated using a combination of descriptive statistics from the data set and constants and formulas that are unique to each type of control chart. A control chart has both an upper control limit and a lower control limit, although on some control charts the lower limit is automatically set at zero and does not change. Generally, the control limits are set near the plus or minus three standard deviation value for the data set.

A good rule of thumb is to not start calculating control limits until you have at least 30 data points. The control limits calculated from fewer points will likely be close, but they don’t become fully stable until approximately that number of points are included.

There are a number of rules that are used for identifying the presence of special cause variation. These rules are similar to those used for the “Run Chart.” However, the values are different. That is because of the statistical nature of the control chart and the inclusion of control limits, which are not calculated for Run Charts.

- Data points that are above the upper control limit or below the lower control limit. These are extreme or astronomical points.
- Nine consecutive data points above or below the mean. This indicates a shift in the mean of the data set.
- Six consecutive data points that are either all increasing or all decreasing. These indicate a trend in the data.
- Fourteen consecutive data points that reverse direction – being up then down as compared to the preceding point. This is a sawtooth pattern and is similar to the “runs” rule used in the Run Chart.

When manually generating the control charts, you will need to apply the rules after each data point is included to see if they have been violated. These rules can be easily set or modified within Minitab. Minitab will then monitor the data and indicate a rule violation by turning the color of the point to red.

### Hints & tips

- Be sure to recalculate the control limits after making a process change or removing the root cause of a special cause variation.
- There are alternate schools of thought that usually slightly different levels for the special cause rules. If your organization uses different values (for instance using just eight data points for the “shift” rule instead of nine), modify the level in Minitab. Follow local practice.
- The specific calculation of control limits will be addressed in the module on each of the different types of control charts.

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