What does it mean if an observation falls outside the control limits?

Control charts determine if a process is in a state of statistical control.

A control chart plots a quality characteristic statistic in a time-ordered sequence. A center line indicates the process average, and two other horizontal lines called the lower and upper control limits represent process variation.

All processes have some natural degree of variation. A control chart for a process that is in-control has points randomly distributed within the control limits. That is it has variation only from sources common to the process (called common-cause variation). An out-of-control process has points falling outside the control limits or non-random patterns of points (called special-cause variation).

If the process is in-control, no corrections or changes to the process are needed.

If the process is out-of-control, the control chart can help determine the sources of variation in need of further investigation. It is appropriate to determine if the results with the special-cause are better than or worse than results from common causes alone. If worse, then that cause should be eliminated if possible. If better, it may be appropriate to investigate the system further as it may lead to improvements in the process.

Typically control limits are defined as a multiple of the process sigma. For a Shewhart control chart with 3-sigma control limits and assuming normality, the probability of exceeding the upper control limit is 0.00135 and the probability of falling below the lower control limit is also 0.00135. Their sum is 0.0027 (0.27%). Therefore the probability of a point between the control limits for an in-control process is 0.9973 (99.73%). An alternative is to define the control limits as probability limits based on a specified distribution rather than assuming a normal distribution.

Another way to look at the performance of a control chart is the average run length (ARL). An average in control run length is the number of observations when a process is in-control before a false alarm occurs. An average out of control run length is the number of observations that a process is out-of-control before a shift is detected, and depends on the size of the shift to be detected. The Shewhart control chart described above has an ARL = 1/0.0027 = 370.37. That is, when a process is in control, you should expect a false alarm out-of-control signal approximately once every 371 runs.

Although most examples of control charts show quality characteristics that are of interest to the end-user (such as length, diameter, or weight) they are most beneficial applied to process variables further upstream (such as the temperature of the furnace or content of tin in the raw material).

Note: It is important not to confuse control limits used in control charts with specification limits used in process capability. Natural variation in a process defines the control limits. Whereas, customer requirements define the specification limits. Likewise, the center line should not be confused with a target value.

Quality Glossary Definition: Control chart

Also called: Shewhart chart, statistical process control chart

The control chart is a graph used to study how a process changes over time. Data are plotted in time order. A control chart always has a central line for the average, an upper line for the upper control limit, and a lower line for the lower control limit. These lines are determined from historical data. By comparing current data to these lines, you can draw conclusions about whether the process variation is consistent (in control) or is unpredictable (out of control, affected by special causes of variation). This versatile data collection and analysis tool can be used by a variety of industries and is considered one of the seven basic quality tools.

Control charts for variable data are used in pairs. The top chart monitors the average, or the centering of the distribution of data from the process. The bottom chart monitors the range, or the width of the distribution. If your data were shots in target practice, the average is where the shots are clustering, and the range is how tightly they are clustered. Control charts for attribute data are used singly.

• When to use a control chart
• Basic procedure
• Create a control chart
• Control chart resources

Control Chart Example

When to Use a Control Chart

• When controlling ongoing processes by finding and correcting problems as they occur
• When predicting the expected range of outcomes from a process
• When determining whether a process is stable (in statistical control)
• When analyzing patterns of process variation from special causes (non-routine events) or common causes (built into the process)
• When determining whether your quality improvement project should aim to prevent specific problems or to make fundamental changes to the process 

Basic Procedure

1. Choose the appropriate control chart for your data.
2. Determine the appropriate time period for collecting and plotting data.
3. Collect data, construct your chart and analyze the data.
4. Look for "out-of-control signals" on the control chart. When one is identified, mark it on the chart and investigate the cause. Document how you investigated, what you learned, the cause and how it was corrected.

   Out-of-control signals

   • A single point outside the control limits. In Figure 1, point sixteen is above the UCL (upper control limit).
   • Two out of three successive points are on the same side of the centerline and farther than 2 σ from it. In Figure 1, point 4 sends that signal.
   • Four out of five successive points are on the same side of the centerline and farther than 1 σ from it. In Figure 1, point 11 sends that signal.
   • A run of eight in a row are on the same side of the centerline. Or 10 out of 11, 12 out of 14, or 16 out of 20. In Figure 1, point 21 is eighth in a row above the centerline.
   • Obvious consistent or persistent patterns that suggest something unusual about your data and your process.

   Figure 1 Control Chart: Out-of-Control Signals

5. Continue to plot data as they are generated. As each new data point is plotted, check for new out-of-control signals.
6. When you start a new control chart, the process may be out of control. If so, the control limits calculated from the first 20 points are conditional limits. When you have at least 20 sequential points from a period when the process is operating in control, recalculate control limits.

Create a control chart

See a sample control chart and create your own with the control chart template (Excel).

Control Chart Resources

You can also search articles, case studies, and publications for control chart resources.

Books

The Quality Toolbox

Innovative Control Charting

Improving Healthcare With Control Charts

Case Studies

Using Control Charts In A Healthcare Setting (PDF) This teaching case study features characters, hospitals, and healthcare data that are all fictional. Upon use of the case study in classrooms or organizations, readers should be able to create a control chart and interpret its results, and identify situations that would be appropriate for control chart analysis.

Quality Quandaries: Interpretation Of Signals From Runs Rules In Shewhart Control Charts (Quality Engineering) The example of Douwe Egberts, a Dutch tea and coffee manufacturer/distributor, demonstrates how run rules and a Shewhart control chart can be used as an effective statistical process control tool.

Articles

Spatial Control Charts For The Mean (Journal of Quality Technology) The properties of this control chart for the means of a spatial process are explored with simulated data and the method is illustrated with an example using ultrasonic technology to obtain nondestructive measurements of bottle thickness.

A Robust Standard Deviation Control Chart (Technometrics) Most robust estimators in the literature are robust against either diffuse disturbances or localized disturbances but not both. The authors propose an intuitive algorithm that is robust against both types of disturbance and has better overall performance than existing estimators.

Videos

Control Chart

Excerpted from The Quality Toolbox, ASQ Quality Press.

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