C chart

C chart
See also
Central tendency Run chart Continuous distribution Check digit Influence diagram Kurtosis Confidence level Coefficient of determination Harmonic mean

A C chart is a type of control chart used to monitor the number of nonconformities in a process. It is used to monitor the number of nonconforming items in a sample. This chart is used when the number of nonconforming items is counted, rather than continuous data such as measurements. The C chart provides information about process variability, as well as the ability to detect changes in process when they occur.

The C chart is a control chart that plots the count of nonconforming items over time. Its purpose is to detect changes in the number of nonconforming items in a process. The chart is constructed by plotting the number of nonconforming items each time a sample is taken. The upper and lower control limits are determined from the data, and any points that fall outside of the limits are considered to be statistically different from the process mean.

The C chart is a powerful tool for detecting small changes in the number of nonconforming items in a process. It provides a way to monitor process performance and detect changes in process when they occur. By monitoring the C chart, it is possible to identify and correct process problems before they become serious.

Formula of C chart

The formula for the C chart is as follows:

$CChart={\frac {NumberofNonconformities}{SampleSize}}$

The C chart is used to calculate the number of nonconforming items in a sample. The formula takes the number of nonconforming items and divides it by the sample size. This calculation provides a measure of process variability, as well as the ability to detect changes in process when they occur.

When to use C chart

The C chart should be used when:

• The number of nonconformities in a sample is counted, rather than continuous data such as measurements.
• Monitoring process performance and detecting changes in process when they occur is important.
• The process needs to be able to detect small changes in the number of nonconforming items.

The C chart is a useful tool for monitoring the number of nonconformities in a process and detecting changes when they occur. It is particularly useful when the number of nonconformities in a sample is counted, rather than continuous data such as measurements. By monitoring the C chart, it is possible to identify and correct process problems before they become serious.

Types of C chart

There are two types of C charts, the standard C chart and the cumulative sum (CUSUM) chart.

• The standard C chart is used to monitor the number of nonconformities in a process over time. It plots the number of nonconformities each time a sample is taken, and the upper and lower control limits are determined from the data.
• The cumulative sum (CUSUM) chart is used to detect small changes in the number of nonconformities in a process. It plots the cumulative sum of the nonconformities over time, and the upper and lower control limits are determined from the data.

Steps of C chart

• Calculate the sample size: The first step in creating a C chart is to calculate the sample size for the data. This can be done by dividing the total amount of data by the number of samples that will be taken.
• Calculate the average number of nonconformities: The next step is to calculate the average number of nonconformities in the sample. This can be done by dividing the total number of nonconformities by the sample size.
• Calculate the upper and lower control limits: The upper and lower control limits for the C chart are calculated using the average number of nonconformities and the sample size. The upper control limit (UCL) is calculated by multiplying the average number of nonconformities by 3, while the lower control limit (LCL) is calculated by multiplying the average number of nonconformities by 1.
• Plot the data: The final step is to plot the data on the C chart. The data should be plotted in the form of a line, with the x-axis representing the sample and the y-axis representing the number of nonconformities. Any points that fall outside of the upper and lower control limits should be investigated further.

Advantages of C chart

• The C Chart is effective for monitoring small changes in the number of nonconforming items in a process.
• It is simple to construct and understand.
• The C Chart provides a way to detect changes in process when they occur.
• The C Chart can be used to identify and correct process problems before they become serious.

Disadvantages of C chart

• The C Chart is only useful when the number of nonconforming items is counted, and not when continuous data such as measurements are used.
• The C Chart is only effective when the sample size is large enough to provide reliable data.
• The C Chart is not suitable for processes with low variability, as the control limits may be too close together to detect small changes.

Although the C chart is a powerful tool for monitoring a process, it does have some limitations. The C chart can only detect changes in the number of nonconforming items, and is not able to detect changes in the size or severity of the nonconformities. Additionally, the C chart is sensitive to sample size, and therefore it is important to ensure that the sample size is appropriate for the process being monitored.

Other approaches related to C chart

In addition to the C chart, there are other approaches to monitoring the number of nonconformities in a process. These include:

• P Chart: This chart is used to monitor the percentage of nonconforming items in a sample.
• U Chart: This chart is used to monitor the number of nonconformities per unit of measure.
• NP Chart: This chart is used to monitor the average number of nonconformities per unit of measure.

These approaches can be used to complement the C chart and provide additional insight into the nonconformity rate in a process.

In conclusion, the C chart is a useful tool for monitoring the number of nonconformities in a process. It provides a way to detect small changes in the process when they occur and can help identify and correct process problems before they become serious. Additionally, there are other approaches that can be used in conjunction with the C chart to provide additional insight into the nonconformity rate in a process.

Suggested literature

• Şentürk, S., & Antucheviciene, J. (2017). Interval type-2 fuzzy c-control charts: an application in a food company. Informatica, 28(2), 269-283.
• Inghilleri, R., Lupo, T., & Passannanti, G. (2015). An effective double sampling scheme for the c control chart. Quality and Reliability Engineering International, 31(2), 205-216.
• Alakoc, N. P., & Apaydin, A. (2018). A fuzzy control chart approach for attributes and variables. Eng. Technol. Appl. Sci. Res, 8(5), 3360-3365.