Guide: Control Charts
- Last Updated: June 11, 2023
Control charts stand as a pivotal element in the realm of statistical process control (SPC), a key component in quality management and process optimization. These charts offer a visual representation of process performance over time, plotting measured data points to track variations, identify abnormalities, and discern trends.
Their primary function is to highlight uncontrolled variations which are deviations from the norm often attributed to external factors. This insightful identification is crucial in determining whether a process is stable and predictable, or in need of refinement. Developed in the 1920s by Walter A. Shewhart, control charts have revolutionized the ability to distinguish between common and special cause variations, enhancing the precision of process evaluation and improvement.
Table of Contents
What Are Control Charts?
Control charts are key statistical tools used in statistical process control (SPC), which is used for quality management and process optimization. Control charts are used as a way to display the performance of a process over time. This is done by plotting the measured output data points on a chart, allowing those viewing them to track how a process varies over time and identify any abnormalities, special-cause variation, or trends. The main reason control charts are used is to highlight any uncontrolled variations; these are variations that are outside the normal operation and can be the result of external or special factors. This identification helps in understanding if a process is stable and predictable or if it requires action for improvement.
Control charts were introduced by Walter A. Shewhart in the 1920s, bringing about a significant advancement in quality control. The main concept of control charts is being able to distinguish between common and special cause variations.
Common Cause Variation: This type of variation is inherent to the process. It’s the “noise” within the system, caused by factors that are usually consistent and predictable over time. This can be seen as the variation that appears inside the upper and lower control limits on the chart above.
Special Cause Variation: In contrast, this variation arises from external factors and is not part of the usual process. It indicates issues that need to be addressed to maintain the quality and consistency of the process. These can be seen with data points that appear outside of the upper and lower control limits.
By effectively identifying these variations, organizations can pinpoint areas requiring improvement and work towards enhancing their overall process stability and quality.
Types of Control Charts
Control charts are categorized based on the nature of the data they manage – variable (quantitative) or attribute (qualitative).
Variable Data Control Charts: These charts are designed for data that can be measured on a continuous scale, such as time, weight, distance, or temperature. They’re ideal for tracking changes in the mean, or variability, of a process. The most common types are:
- X-bar and R Chart: Used to monitor the mean (average) and range (variability) of a process. Suitable for small sample sizes.
- X-bar and S Chart: Similar to the X-bar and R chart but more appropriate for larger sample sizes, as it monitors the mean and the standard deviation of a process.
Attribute Data Control Charts: These charts are used for data that are not measured but counted, typically focusing on items that are either conforming or non-conforming. They include:
P Chart (Proportion Chart): Used to track the proportion of defective items in a sample. It’s useful when the sample size varies and the data is expressed as a proportion.
C Chart (Count Chart): This chart is used to monitor the count of defects or nonconformities in an item or a unit. It’s useful when the number of opportunities for defects is constant.
Components of a Control Chart
A control chart is more than just a line graph; it’s a sophisticated tool designed for process monitoring and improvement. Understanding its components is key to leveraging its full potential:
- Data Points: These are the core of the control chart, representing individual measurements or values collected from the process over time. Data points are plotted sequentially, usually along the vertical axis, against the time or sequence order on the horizontal axis. They provide a visual representation of how the process performs over time and are the basis for further analysis.
- Center Line: Typically, this is the process mean (average), or sometimes the median. It acts as a reference line around which data points are expected to fluctuate. The center line is crucial as it reflects the ‘normal’ performance level of the process where it should be operating if everything is stable and no special causes of variation are present.
- Control Limits: These limits define the boundary of expected process variation and are set at ±3 standard deviations from the center line. The choice of three standard deviations is statistically significant as it covers about 99.73% of the data points in a normal distribution, assuming the process is under control. The area within the control limits represents normal process variation (common cause variation), while points outside these limits indicate unusual variation (special cause variation) that may necessitate investigation.
- Out-of-Control Signals: These are indications that the process might be out of control. They are identified when data points fall outside the control limits or when they exhibit non-random patterns within the limits (like a series of points steadily increasing or decreasing). Such signals prompt further investigation to identify and correct the root causes of the variation.
How to Create a Control Chart
Step 1: Data Collection
To create a control chart, you first need data. You may already have this data, but consider that it needs to be gathered sequentially over a set period to reflect the process’s typical operation. It is also important that the data be as accurate and unbiased as possible.
When constructing a control chart, the amount of data collected is crucial and should be tailored to the specifics of the process. For most situations, gathering at least 20-25 subgroups, each with 4-5 individual measurements, is a good starting point. In total, aim for a minimum of 100 data points to establish a reliable baseline.
The data should be collected consistently over time, with the frequency and volume adjusted based on the process’s stability and output rate. It’s important to balance the need for precision and confidence in the results with the practicality of data collection. As you gain more insights into the process, be prepared to adapt your data collection strategy to ensure it adequately reflects the process’s variability and your analysis needs.
Step 2: Calculate the Center Line
The next step is to establish a baseline for the process’s performance. The centerline is usually the mean (average) of the data set. The mean is calculated by adding all of the data points and dividing by the number of data points. This line will then be used as a reference point to compare individual data points and indicate the average performance of the process.
Step 3: Determine the Control Limits
Next, we need to determine the control limits (boundaries of expected process variation). Control limits are set at three standard deviations (σ) from the mean. If you are not sure how to calculate the standard deviation, take a look at our standard deviation guide, as it is key to creating and understanding control charts. You can also use our standard deviation calculator for a quick answer to calculating the standard deviation, which you can multiply by three.
To calculate control limits for a control chart, first determine the process mean and standard deviation from your data. For example, if your process mean (average) is 50 and the standard deviation is 5, the Upper Control Limit (UCL) is calculated as the mean plus three times the standard deviation (3 x 5 = 15), therefore (50 + 35 = 65), and the Lower Control Limit (LCL) as the mean minus three times the standard deviation (50 – 35 = 35). These limits represent the boundary of normal variation for a process in control. Data points outside these limits suggest special-cause variations, indicating a process that may be out of control.
Step 4: Plot the Data
Once you have your data and have calculated the mean, the standard deviation, and the control limits, the next step is to plot the chart. You can create a control chart in Microsoft Excel by setting your data out like in the example image and following these steps
- Select the Data
- Click Insert
- Click the line chart
- Select the first 2-D line chart
Alternatively, you can try our Control Chart analyzer tool, which will allow you to upload your data and get instant detailed analysis of observations and feedback of your data. Just like in the example below
Step 5: Interpret the Chart
The final step involves analyzing the control chart. Interpreting a control chart involves closely examining it for data points that fall outside the established control limits or for specific patterns within these limits. Data points beyond the control limits are indicators of special cause variations, signifying an anomaly in the process that may require investigation. Additionally, even if points are within the control limits, certain patterns, such as consistent upward or downward trends, cycles, or too much clustering, can signal underlying issues. These patterns might point to potential areas for process improvement, highlighting the need for further analysis to understand and address the root causes.
How to Analyze a Control Chart
Recognizing Patterns
- Shifts: Consist of eight or more consecutive points on one side of the center line. This could indicate a significant change in the process.
- Trends: Involve six or more consecutive points either increasing or decreasing. Trends can suggest a gradual change in the process.
- Cycles: These are repeating patterns of points. They might indicate seasonal effects or other recurring factors affecting the process.
Acting on Analysis
- Investigate Causes: When any of these patterns are identified, it’s important to investigate the underlying causes. This could involve looking into changes in materials, machinery, methods, or the environment.
- Implement Changes: Once the cause is identified, appropriate changes can be made to correct or improve the process.
- Monitor Effects: After implementing changes, continue to use the control chart to monitor the process and ensure that improvements are sustained.
Conclusion
Control charts are indispensable in the toolkit of quality control, providing a systematic and visual approach to monitoring process stability and identifying areas for improvement. By plotting data points, establishing a center line, setting control limits, and interpreting the resulting chart, these tools enable the detection of special cause variations and the observation of patterns such as shifts, trends, and cycles.
Through careful analysis and subsequent actions based on these insights, control charts empower organizations to proactively address underlying issues, optimize processes, and maintain high-quality standards. The ultimate goal is not just to identify and rectify problems but to foster an environment of continuous process improvement and sustained operational excellence.
References
- Lowry, C.A. and Montgomery, D.C., 1995. A review of multivariate control charts. IIE transactions, 27(6), pp.800-810.
- Woodall, W.H., Spitzner, D.J., Montgomery, D.C. and Gupta, S., 2004. Using control charts to monitor process and product quality profiles. Journal of Quality Technology, 36(3), pp.309-320.
Q: What is a control chart?
A: A control chart is a statistical tool used to monitor and analyze a process over time. It helps determine if a process is in control or if there are any special causes of variation present.
Q: How does a control chart work?
A: A control chart consists of a graph with data points plotted over time. It typically includes a centerline representing the process average and control limits that define the acceptable range of variation. Data points falling within the control limits indicate that the process is stable, while points outside the limits may suggest the presence of special causes of variation.
Q: What are the benefits of using control charts?
A: Control charts provide several benefits, including:
- Early detection of process changes or deviations.
- Identification of special causes of variation.
- Reduction in process variability.
- Improvement in process performance and quality.
- Objective data-based decision making.
- Effective communication of process performance to stakeholders.
Q: What are the types of control charts?
A: There are various types of control charts, including:
- Individuals control chart: Used when individual data points are measured.
- X-bar and R chart: Utilized when data is collected in subgroups, and both the subgroup averages (X-bar) and ranges (R) are tracked.
- X-bar and S chart: Similar to the X-bar and R chart, but it uses the standard deviation (S) instead of the range (R) to measure variation.
- p-chart: Used for monitoring the proportion of nonconforming items or defects in a process.
- np-chart: Similar to the p-chart but used when the sample size is constant.
- c-chart: Used when the count of defects per unit is measured.
Q: How do you interpret a control chart?
A: When interpreting a control chart, the following guidelines are generally followed:
- Data points within the control limits suggest a stable and predictable process.
- Points outside the control limits may indicate the presence of special causes of variation.
- Nonrandom patterns or trends, such as consecutive points on one side of the centerline, could suggest process shifts or other issues.
- It is important to investigate and address points beyond the control limits or any unusual patterns to identify and eliminate special causes.
Q: What is meant by "common cause" and "special cause" variation?
A: “Common cause” refers to the natural variation that is inherent in a process and expected to occur randomly. It is also known as “normal” or “chance” cause variation. Control charts help identify and quantify this type of variation.
“Special cause” refers to unusual or non-random sources of variation that are not inherent to the process. These causes are typically assignable to specific factors or events and can lead to unexpected changes in the process output. Control charts help detect and investigate these special causes so that appropriate actions can be taken.
Q: Can control charts be used in any industry or process?
A: Yes, control charts can be used in various industries and processes where data is collected over time. They are commonly applied in manufacturing, healthcare, finance, software development, and service industries to monitor and improve process performance.
Q: What are the limitations of control charts?
A: Control charts have a few limitations, including:
- They rely on accurate and reliable data collection and measurement.
- Control charts assume that the process is in a state of statistical control at the beginning.
- Control charts may not identify small shifts or changes in a process if the sample size is small.
- Control charts do not identify the specific causes of variation; they only signal when variation is present.
- Control charts may not be effective in detecting certain types of non-random patterns or complex interactions among process variables.
Q: Are there software tools available for creating and analyzing control charts?
A: Yes, there are many software tools available that can help create and analyze control charts. Some popular options include Minitab, JMP, Excel with add-ins like QI Macros, and various statistical software packages like R and Python that have control chart libraries and functions. These tools make it easier to plot control charts, calculate control limits, and perform statistical analyses.
Author
Daniel Croft
Daniel Croft is a seasoned continuous improvement manager with a Black Belt in Lean Six Sigma. With over 10 years of real-world application experience across diverse sectors, Daniel has a passion for optimizing processes and fostering a culture of efficiency. He's not just a practitioner but also an avid learner, constantly seeking to expand his knowledge. Outside of his professional life, Daniel has a keen Investing, statistics and knowledge-sharing, which led him to create the website learnleansigma.com, a platform dedicated to Lean Six Sigma and process improvement insights.
Free Lean Six Sigma Templates
Improve your Lean Six Sigma projects with our free templates. They're designed to make implementation and management easier, helping you achieve better results.
