Which control chart would you use to track the number of defects found when the sample size is constant?

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.

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.
   • 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.

A Control Chart shows how a process varies over time while identifying special causes of variation and changes in performance. Similar to a run chart, it includes statistically generated upper and lower control limits. This type of chart prevents changing a process that is varying randomly within the control limits (no special cause present). Variables data in a control chart measure units in length, temperature, etc.

Purpose of Control Charts

The purpose of a control chart is to show Program Managers and project personnel if a process is varying over time which will allow them to correct those processes if needed.

Best Time to Use a Control Chart

Determining the best time to use a control chart is important.  The following is a list of when it’s a good time to use a control chart.

• Analyzing ongoing processes by find anomalies
• Predicting the expected range of outcomes from a process
• Determining if a process is stable over time
• Analyzing patterns in a process
• Making a decision to fix a problem or change the process

When Not to Use a Control Chart

Unless the process question is clearly identified and the data supports an investigation of the process to control, control charts should not be the first tool used to analyze data.

Steps in Developing a Control Chart

Developing a control chart involves the following list of steps and activities:

• Step 1: Determining the type of chart needed,
• Step 2: Constructing the chart based upon the type of data,
• Step 3: Identifying and eliminating any special or assignable causes of variation,
• Step 4: Collecting 20 to 30 subgroups of data (consisting of two or more data points),
• Step 5: Determining the average and the range for each subgroup,
• Step 6: Determining the overall means (also called the grand average),
• Step 7: Determining the average value of the range,
• Step 8: Calculating the control limits and centerlines
• Step 9: Plotting the charts
• Step 10: Recalculating the control limits if there is a significant change in the process average or variability

Control Charts use two types of data:

1. Attributes: A specific value or characteristic that is either present or absent and can be counted, but not measured. Attributes data requires making good/bad or go/no-go decisions and then counting this data, which is easier and less costly to obtain. There are typically four (4) types of attribute control charts:
   • np chart: Charts the number of defective units in a subgroup if the sample size is constant.
   • p chart: Charts the fraction or percent defective if the sample size varies.
   • c chart: Charts the number of defects in a subgroup if the sample size is constant.
   • u chart: Charts the number of defects per unit if the sample size varies.
2. Variables: Data that requires measurements of an actual value rather than simple counting. Variables data needs measurements in units such as length, temperature, etc. The data is harder to obtain, but the charts better control a process. There are typically two (2) types of attribute control charts:
   • XmR chart: Chart is used when there is only one observation in each time period.
   • x-R chart: Charts to monitor a variable’s data when samples are collected at regular intervals from a business or industrial process.

Control Chart Negative Outcomes

Defective: A unit that fails to meet acceptance criteria due to one or more defects. Defective data is used when a quality characteristic of an item cannot be easily measured but can be classified as conforming or non-conforming. It involves the fraction, or percent of defectives in a sample, and are represented in either an np chart or an n chart.

Defect: A failure to meet one part of the acceptance criteria. Defect data is used when the quality of the item can be determined by the number of defects in the item or by counting the number of occurrences of some event per unit of time. The data can be shown in either the c chart or the u chart.

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Updated: 7/11/2021

Rank: G27.2