# C Chart

## What is C Chart?

A C Chart, also known as a count chart or a frequency chart, is a statistical quality control chart that is used to monitor the number of non-conformities or defects in a sample or a process. It is a type of attribute control chart that is commonly used in manufacturing industries, such as automobile, electronics, and textiles, to detect and correct problems before they lead to quality issues.

The C Chart is constructed by plotting the number of defects or non-conformities in each sample or subgroup over time or production runs. The chart has two control limits, an upper control limit (UCL) and a lower control limit (LCL), which are calculated based on the average number of defects or non-conformities in the historical data. The limits represent the boundaries of acceptable performance, and any data points outside the control limits indicate that the process is out of control and requires corrective action.

## When to use C Chart?

C chart is particularly useful in situations where the subgroup size is relatively small and where there is a low expected number of defects or nonconformities. They are also suitable for use when the occurrence of defects or nonconformities is rare events.

Therefore, the C chart is suitable for monitoring the count of defects or nonconformities in manufacturing processes, customer complaints, hospital readmissions, etc.

## Guidelines for correct usage of C Chart

• Count the number of defects on each item or unit.
• Use appropriate charts based on whether the data is defective or non defective.
• Consider using U chart if your data exhibits over dispersion or under dispersion.
• Collect data in time order and at equally spaced time intervals.
• Collect data in subgroups that are representative of the output from the process.
• Subgroup sizes should be equal or nearly equal. Use U Chart if subgroup sizes are not equal.
• The subgroups must be large enough to obtain accurate control limits.
• Collect enough subgroups to obtain precise control limits.

## Alternatives: When not to use C chart

• Use U Chart when subgroup sizes are not equal.
• For data that only indicate whether each item is defective or non defective, use P Chart to plot the proportion of defective items or use NP Chart to plot the number of defective items.
• A C Chart may show an increased number of points outside the control limits due to over dispersion, or too few points outside the control limits due to under dispersion. You can use the U Chart Diagnostic to test for over dispersion and under dispersion.

## Example of C Chart?

The stability of the wallpaper printing process is being evaluated by a quality engineer. Every hour, the engineer takes a 100-foot wallpaper sample and counts the number of printing defects, which includes missing ink, print smears, and pattern distortions. She has performed the analysis in following steps:

1. She worked all day and gathered the data.

1. After gathering the data, she uses mathematical formula for finding the mean of all the defects present. The mean is denoted by c bar and its value is 36.68
2. After calculating this, she calculates Upper Control Limit (UCL) and Lower Control Limit (LCL).
3. Now, after calculating c bar, UCL and LCL, she analyzes the data with the help of https://qtools.zometric.com/
4. After using the above mentioned tool, she fetches the useful graph as follows:

## How to generate C Chart?

The guide is as follows:

1. Login in to QTools account with the help of https://qtools.zometric.com/
2. On the home page, one will see C Chart under control charts.
3. Click on C Chart and will reach the dashboard.
4. Next, update the data manually or can completely copy (Ctrl+C) the data from excel sheet and paste (Ctrl+V) it here.
5. Next, you need to select the desired Check Rules.
6. Finally, click on calculate at the bottom of the page and you will get desired results.

On the dashboard of C Chart, the window is separated into two parts.

On the left part, Data Pane is present. Data can be fed manually or the one can completely copy (Ctrl+C) the data from excel sheet and paste (Ctrl+V) it here.

On the right part, there are many options present as follows:

• Process mean: If process mean is provided, this value is considered to be the centerline. If not, Zometric Q-Tools calculates the centerline from the data provided.
• Use unbiasing constants for pooled sd: This option is applicable only when Stdev is estimated using Pooled Stdev method.
• Check Rule 1: 1 point > K Stdev from center line : If a data point is K standard deviations from the center line, it means that it is K times the standard deviation away from the mean. This is important in statistical process control because it indicates whether a data point is within acceptable limits or whether there may be a problem with the process that needs to be addressed. Typically, data points that are more than three standard deviations from the center line are considered outliers and may require further investigation.
• Check Rule 2: K points in a row on same side of center line : If there are K points in a row on the same side of the center line in a dataset, it suggests that there may be a bias or trend in the data that is causing the values to cluster together. This could be due to a variety of factors, such as measurement error, sampling bias, or a true underlying pattern in the data.
• Check Rule 3: K points in a row, all increasing or all decreasing: If there are K points in a row, it is certain that at least one of two things must be true:
• The points are all increasing (i.e. each point has a greater y-coordinate than the one before it)
• The points are all decreasing (i.e. each point has a smaller y-coordinate than the one before it)
• Check Rule 4: K points in a row, alternating up and down:
• If the trend is upwards, it indicates that the process is becoming less consistent and more variable over time. This can be caused by factors such as equipment deterioration, operator error or changes in raw material quality.
• If the trend is downwards, it indicates that the process is becoming more consistent and less variable over time. This could be due to process improvements or tighter control measures being implemented.