# Control Charts

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Skip to content # Control Charts

#### Table of Contents

## Control Chart, What is it?

### What is a Control Chart?

### Types of Control Charts?

### How to Select the Right Type of Control Chart?

## Features of a Control Chart

### Control Limits and how they are Calculated

### Example of Calculated Control Limits

## How to use a Control Chart

### Steps for Creating a Control Chart

### How to Identify and Address Special Causes Variations

## Benefits of a Control Chart

### Improved Process Stability and Predictability

### Identifying and Addressing Process Issues Quickly

### Facilitating Continuous Improvement Efforts

## Conclusion

## What's Next?

#### Course Index

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- Lean six Sigma Yellow Belt Course
- Control Charts

Control charts are a key element in the DMAIC process’s control step (Define, Measure, Analyze, Improve, Control). They are used to monitor and improve a process’s stability and predictability. In this module, we will discuss control charts, their features, how to utilise them, and the benefits they can give. Organizations can detect and address issues with their processes by understanding and applying control charts, ultimately leading to greater performance and customer satisfaction.

A control chart is a graphical representation of data that is used to track the progress of a process over time. It is a statistical tool that aids in the identification of patterns and variations in data, providing insight into the stability and predictability of a process. Control charts are used to determine whether a process is in statistical control, which means that it is stable and predictable, or if there are special cause variations that must be addressed.

Control charts include a centerline that represents the process average, as well as upper and lower control limits calculated using statistical formulas. The data points on the chart are plotted and compared to the control limits. If the data points fall within the control limits, the process is said to be in statistical control. If data points exceed the control limits, it may indicate that there is a special cause variation that must be addressed.

There are several types of control charts that are commonly used to monitor various types of data. Some of the most common types are:

**X-bar and R chart:**This type of control chart is used to track the mean and variability of a process over time. It is commonly used for continuous data such as measurements, weights, and times.**P chart:**This type of control chart is used to track the proportion of defective items in a process. It is commonly used for discrete data such as the number of defects per unit or the number of defective items per batch.**C chart:**This type of control chart is used to track the number of times an event or condition occurs. It is frequently used to count data such as the number of customer complaints or machine breakdowns.

Organizations can gain a better understanding of their processes, identify patterns and variations, and make informed decisions to improve process performance by using the appropriate type of control chart.

The type of control chart to use is determined by the type of data being collected and analysed. Here are some pointers to help you decide which type of control chart to use:

- An X-bar and R chart is commonly used for continuous data such as measurements, weights, and times.
- A P chart may be more appropriate for discrete data, such as the number of defects per unit or the number of defective items per batch.
- A C chart may be more appropriate for counting data, such as the number of customer complaints or machine breakdowns.
- A U chart can be used to display attribute data such as pass/fail or go/no-go.

When choosing a control chart, it is also important to consider the subgroup size. When the subgroup size is small, an XmR chart can be used, where X represents the mean of each subgroup and R represents the range of each subgroup. When the subgroup size is large, an Xbar-S chart can be used, where S is the standard deviation of each subgroup.

It is also important to note that control charts should not be used with data that is not normally distributed or has a high degree of autocorrelation. Other statistical methods may be more appropriate in these cases.

It’s always a good idea to consult with a statistician or a Six Sigma expert who can help you choose the best control chart for the data you have and the purpose of the analysis.

Statistical formulas are used to calculate the control limits. For example, in an X-bar and R chart, a type of continuous data control chart, the control limits for the X-bar chart (the chart that plots the mean of each subgroup) are calculated using the following formulas:

Upper control limit (UCL) = X-bar + A2Rbar

Lower control limit (LCL) = X-bar – A2Rbar

Where X-bar is the average of the subgroup means, Rbar is the average of the subgroup ranges, and A2 is a sample size-dependent constant.

It’s important to note that the control limits are calculated under the assumption that the process is stable and under statistical control, which means that it’s working properly. If special cause variations exist, the control limits may not accurately reflect the expected range of variation, so these variations must be investigated and addressed accordingly.

Here’s an example of a control limit calculation using an X-bar and a R chart:

Assume we are measuring the weight of a product as it leaves an assembly line. Every hour, we take a sample of 5 products and weigh them. These samples are used to compute the X-bar and R values for each hour.

To obtain the X-bar values, we first compute the average of the five product weights for each hour.

Hour 1: X-bar = (20 + 21 + 22 + 20 + 19) / 5 = 20.4

Hour 2: X-bar = (19 + 21 + 22 + 21 + 20) / 5 = 20.4

Hour 3: X-bar = (21 + 22 + 23 + 22 + 21) / 5 = 21.8

Hour 4: X-bar = (22 + 23 + 24 + 23 + 22) / 5 = 22.8

Hour 5: X-bar = (21 + 22 + 23 + 22 + 21) / 5 = 21.8

Next, we calculate the range (R) of the product weights for each hour. The range is the difference between the largest and smallest value in the sample.

Hour 1: R = 22 – 19 = 3

Hour 2: R = 21 – 19 = 2

Hour 3: R = 23 – 21 = 2

Hour 4: R = 24 – 22 = 2

Hour 5: R = 23 – 21 = 2

Now we can calculate the control limits for the X-bar chart using the following formulas:

UCL (upper control limit) = X-bar + A2Rbar LCL (lower control limit) = X-bar – A2Rbar

Where X-bar is the average of the subgroup means, Rbar is the average of the subgroup ranges, and A2 is a constant that depends on the sample size.

To calculate Rbar, we take the average of all R values Rbar = (3 + 2 + 2 + 2 + 2) / 5 = 2.2

We need to use a table of A2 constant values to find the right value based on the sample size. For a sample of 5, A2=2.66.

Now we can use the above formulas to calculate the control limits for the X-bar chart

UCL = 20.4 + (2.66 * 2.2) = 25.74 LCL = 20.4 – (2.66 * 2.2) = 15.06

So the control limits for the X-bar chart are 25.74 and 15.06. Any data points that fall outside of these limits would indicate that a special cause variation is present and further investigation is needed.

It is important to note that this is only an example calculation; in practise, calculating control limits would typically involve more data points and a longer period of time to ensure the process’s stability. Furthermore, the control limits are recalculated on a regular basis to ensure that they are accurate and reflect the current state of the process.

It’s also worth noting that this example only looks at calculating control limits for the X-bar chart. Control limits for other chart types, such as R charts, P charts, and C charts, must also be calculated in order to fully utilise a control chart. Each chart type is used for a specific type of data, and the appropriate chart must be selected.

It’s also critical to understand that control limits are calculated under the assumption that the process is stable and under statistical control. When there are special cause variations, the control limits may not accurately reflect the expected range of variation. As a result, control charts, along with other statistical tools and techniques, are essential for understanding the process and identifying and addressing any special cause variations that may exist.

Creating a control chart entails several steps, which include:

**Identify the process and the variable to be monitored:** The first step is to identify the process to be tracked and the variable that will be used to track it. It is critical to choose a variable that is directly related to the process and that can be easily and accurately measured.

**Collect data:** Over a period of time, collect data for the variable being monitored. It is critical to collect data at regular intervals, such as every hour, day, or week, to ensure that the process is consistently monitored. It is also critical to collect data in the same way each time to ensure that the data is comparable.

**Organize and analyse the data:** Divide the data into subgroups, with the same number of data points in each. Determine the mean and range for each subgroup.

**Calculate control limits:** Use statistical formulas to calculate the control limits for the variable being monitored. The formulas used will be determined by the type of control chart used.

**Create the control chart:** Create a control chart with the data points, control limits, and centre line.

**Interpret the control chart:** Examine the data for patterns to see if the process is stable and under statistical control. If data points exceed the control limits, it may indicate a problem with the process, which is known as special cause variations, and further investigation is required.

**Monitor and update the control chart:** As new data is collected, continuously monitor the process and update the control chart. Based on the new data and the process stability, adjust the control limits as needed. It is critical to keep an eye on the control chart so that you can detect any changes in the process and take corrective action as soon as possible.

**To make data-driven decisions, use the control chart:** Control charts can be used to identify process areas that need improvement, track progress over time, and assess the effectiveness of any process changes. This can assist you in making data-driven decisions that will improve the process and achieve the desired results.

Finally, it is critical to communicate the results of the control chart analysis to the relevant stakeholders. This will assist them in comprehending the current state of the process and any actions required to improve it. It also assists management in making informed decisions and allocating resources appropriately.

It’s important to remember that creating a control chart is an ongoing process because both the process and the data change over time. As a result, it’s critical to keep an eye on the process and update the control chart as needed.

Variations caused by special causes are those that are not caused by common causes and indicate that something outside of the normal process is affecting the process. Data points that fall outside of the control limits can be used to identify these variations. When a unique cause variation is identified, it is critical to investigate the cause and take appropriate action to address it. Adjusting the process, changing the equipment or materials used, or retraining employees are all examples of this.

In conclusion, control charts are a necessary tool for monitoring and analysing process data. Organizations can effectively identify patterns and variations, interpret control chart patterns, and address special cause variations by understanding the features of control charts, resulting in improved process performance and customer satisfaction.

Control charts are an effective tool for process improvement because they allow you to track process performance over time, identify problems, and make data-driven decisions that can help improve process stability and predictability. In this section, we will go over the advantages of using control charts in greater depth.

One of the most significant advantages of using control charts is improved process stability and predictability. A stable process is one that operates within a consistent range of variation and is less likely to produce unexpected results. This predictability makes identifying patterns and trends that can help improve the process easier.

Control charts, which plot data points and draw control limits, aid in identifying and tracking patterns in the process over time. The upper and lower bounds on a control chart that indicate the expected range of variation for a stable process are known as control limits. When data points fall outside of the control limits, it indicates that there may be a problem with the process and that the cause of the variation must be investigated.

Control charts can help identify and address issues quickly, before they become major problems, by monitoring the process on a regular basis. This allows for the early detection of any issues that may arise, as well as the identification of trends and patterns that can help improve the process.

Furthermore, when a process is under statistical control, it becomes more predictable and easier to identify patterns that can aid in process improvement. A statistically controlled process is one that operates in a consistent and predictable manner, and any variations that occur can be attributed to common cause variation, which is inherent in the process and is to be expected. This predictability enables teams to better understand the process and make data-driven decisions that can help it improve.

Overall, control charts help to improve process stability and predictability by allowing you to track process performance over time, identify issues, and make data-driven decisions.

Another significant advantage of using control charts is the ability to quickly identify and address process issues. Control charts visualise the process, making it easier to identify any variations or issues that may arise. Control charts do this by plotting data points over time and drawing control limits, which indicate the expected range of variation for a stable process. When data points fall outside of the control limits, it indicates that there may be a problem with the process and that the cause of the variation must be investigated.

Control charts can help identify and address issues quickly, before they become major problems, by monitoring the process on a regular basis. This is due to the fact that any problems or variations are immediately visible on the control chart, allowing teams to take action as soon as possible. This is critical because the earlier an issue is identified, the sooner it can be addressed and the less impact it has on the process.

Furthermore, control charts save time and resources by identifying issues early, allowing teams to take action before the problem escalates. This can help to reduce the impact of any issues on the process and prevent future problems from arising. This is due to the fact that when an issue is identified and addressed quickly, it is less likely to cause significant disruptions to the process and fewer resources and time will be wasted attempting to fix the problem.

Finally, control charts are an effective tool for quickly identifying and addressing process issues. Control charts can help teams identify issues early, before they become major problems, by providing a visual representation of the process and monitoring it on a regular basis. This can help save time and resources, as well as reduce the impact of any problems on the process.

“Facilitating continuous improvement efforts” is another key benefit of using control charts. Control charts allow you to assess the effectiveness of any process changes or improvements. This is because control charts track progress over time, allowing you to identify areas for improvement and compare the efficacy of various approaches. This allows teams to identify and address issues as they arise, which can help to foster a culture of continuous improvement within an organisation.

When a process is changed or improved, control charts allow teams to track the progress and measure the effectiveness of the changes. Teams can see if the changes have had a positive impact on the process by monitoring it on a regular basis. Control charts can be used to track progress over time and identify areas that need further improvement as well as evaluate the effectiveness of different approaches.

Furthermore, control charts aid in the development of a culture of continuous improvement within an organisation. This is due to the fact that control charts allow teams to identify and address issues as they arise. When issues are identified early on, teams can take action to address them, and teams can assess the efficacy of various approaches. This enables teams to make data-driven decisions that can help to improve the process, and it contributes to the creation of a culture of continuous improvement in which teams are constantly looking for ways to improve the process.

Besides that, control charts are an effective tool for continuous improvement because they assist teams in better understanding the process. This is because control charts allow teams to identify patterns and trends that can help improve the process by measuring and tracking process performance over time.

Finally, control charts are an effective tool for facilitating continuous improvement efforts. Control charts assist teams in identifying areas that require further improvement and evaluating the effectiveness of various changes or improvements made to the process by providing a way to measure the effectiveness of any changes or improvements made to the process.

To summarise, control charts are an important tool for process improvement because they allow organisations to track process performance over time, identify patterns and variations, and make data-driven decisions to improve process stability and predictability. Control charts help teams identify and address issues quickly, before they become major issues, and they aid in continuous improvement efforts by providing a means to assess the effectiveness of any changes or improvements made to the process.

Control charts of various types, such as X-bar and R charts, P charts, and C charts, can be used to monitor various types of data and provide insights into various aspects of a process. Overall, control charts are an effective tool for improving the performance of any process and should be included in any process improvement strategy.

Hopefully, you now have a basic understanding of Control Charts, but will likely require some practice to use these in your projects. Next, we look at Error Proofing or as the Japanese call it Poka Yoke. Which is preventing defects by design.