Which one of the following control charts would be used to monitor variables data?

Consider that you are evaluating the output from a process.  Conceptually, you could evaluate the products in two basic ways.  In the first way you would simply classify the products as "conforming" or "non conforming."  This produces attribute (discrete) data.  In the second way you could measure a key characteristic using a continuous scale.  This produces variable (continuous) data.

Variables control charts are used to evaluate variation in a process where the measurement is a variable--i.e. the variable can be measured on a continuous scale (e.g. height, weight, length, concentration). There are two main types of variables control charts.  One (e.g. x-bar chart, Delta chart) evaluates variation between samples. Non-random patterns (signals) in the data on these charts would indicate a possible change in central tendency from one sampling period to the next.  One way of thinking about the use of a variables control chart is that you are testing the hypothesis that a particular sample mean came from the population of sample means represented by the control limits of the process.  If the particular sample mean is within the control limits, your concusion is that it does come from that population.  If the particular sample mean is outside the control limits, you conclusion is that it may have come from some other distribution (i.e. a distribution with a mean that is higher or lower than this population mean.  [NOTE:  There are other signals that may indicate an out-of-control signal that will be discussed in the Lesson Six Presentation.]

The other type of variables control chart (e.g. R-chart, S-chart, Moving Range chart) evaluates variation within samples.  Non-random patterns (signals) in the data on these charts would indicate a possible change in the variation within the samples.

Non-random patterns in the data plotted on the control charts provide evidence of the process being in-control (only common cause variation present; predictable) or out-of-control (common cause and assignable cause variation present; unpredictable).  Adjusting a process which is in-control will result in increased variation.  Failing to adjust a process which is out-of-control results in a loss of predictability.  Control charts help a machine operator or manager to decide when it is appropriate to make an adjustment and when it is better to leave the process alone.

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.

What type of control chart is used to monitor variations in a process?

Which control chart should be used for the variable sample size?

Which control chart is used to measure variability of variability with in the sample?

What are the two control charts for variables?