# Control Chart (C Chart) Definition

### Control Chart (C Chart) Definition

The C chart is a type of control chart that is used in the monitoring of count-type data which is usually the total number of conformities per unit. It is also sometimes used in monitoring the sum of events occurring in a given unit of time.

### A Little More on What is Control Charts

When the control chart indicates that the process under monitoring is not under control, the analysis derived from the chart can be useful in determining the sources of this variation because it might cause a degraded performance of the process. A stable process that operates outside the desired limits of specifications needs to be improved through an intentional effort aimed at understanding the causes of the current performance and improve it fundamentally.

The control chart is among the seven basic tools used for quality control. Usually, the control charts are used in the time-series data, but they can also be used for data having logical comparability if there is a desire of comparing the samples that are all taken at the same time, although the type of chart to be used in this case needs a lot of consideration.

Control charts constitute the following:

•         The points which represent a statistic of the measurements of a quality characteristic type present in the samples that are taken at different times of the process.
•         The mean of the statistic in the above step is calculated using all the samples, e.g., the mean of the ranges, the mean of the proportions, and the mean of the means.
•         A center line which is drawn at the value of the mean of the statistic.
•         The standard error of the statistic is also determined with the use of all the samples.
•         The upper control limits and the lower control limits, also known as the natural process limits, indicate the threshold point at which the output of the process is sometimes considered unlikely statistically and then drawn at three standard errors that occur from the central line drawn.

### Types

The control chart builder easily makes the control charts. When creating the chart, it is not necessary to know its name or structure. One only needs to select the column of variables that are to be charted and then drop them in their respective zones. Anytime a data column gets dragged into the workspace the control chart builder begins working on it creating an accurate and relevant chart based on the data type and sample size given.

When the chart has been created, the required changes in type, format or statistics of the chart can be made using the various menus and options.

### Control Charts for Variables

These can be classified per the statistic of subgroup summary plotted on the chart.

### X¯ Chart, R Chart, S Chart

X-chart indicates subgroup averages, R chart shows subgroup ranges and the S chart displays the subgroup standard deviations. A specific analysis makes clear the process mean and its variability together with a mean chart aligned above its corresponding S- or R- chart for the characteristics of quality to be measured on a continuous scale.

### Individual Measurement Charts

These are used to display the measurements individually although they are only appropriate in use at places where only one measurement is made available for every sample or subgroup. When the individual measurements are changed, then the chart also displays above the corresponding moving range chart to it. These moving range charts display the ranges in the movement of two successive measurements.

### Pre-summarize Charts

In case data contains repetitive measurements of the same unit process, they can be combined into one measurement for the unit. However, this is only recommended when the data contains repetitive measurements for every measurement unit or process. These charts summarize the process columns into standard deviations based on the sample size or the chosen label of the sample and then chart the summarized data based on the selected options in the window.

### Levey – Jennings Charts

These show a mean process that is based on a long term sigma with control limits. These control limits are placed in such a way that the distance between them and the center line is ‘3s’. These charts’ standard deviation ‘s’ is calculated similarly to the standard deviation in the distribution platform.

### References for C Chart

https://math.tutorvista.com/statistics/control-charts.html

https://en.wikipedia.org/wiki/C-chart

### Academic Research for C Chart

• The application of control chart for defects and defect clustering in IC manufacturing based on fuzzy theory, Hsieh, K. L., Tong, L. I., & Wang, M. C. (2007). Expert Systems with Applications, 32(3), 765-776. This study introduces a control chart which applies fuzzy theory and engineering experience in the monitoring of wafer defects with the consideration of defect clustering. This control chart is simpler and more rational than the revised c-charts.
• A multivariate exponentially weighted moving average control chart, Lowry, C. A., Woodall, W. H., Champ, C. W., & Rigdon, S. E. (1992). Technometrics, 34(1), 46-53. This paper presents a multivariate extension of the exponentially weighted average control chart and then gives the guidelines for designing the easy-to-implement multivariate procedure.
• A bibliography of statistical quality control chart techniques, 1970–1980, Vance, L. C. (1983). Journal of Quality Technology, 15(2), 59-62. This article presents a search for the literature to find out the status of statistically quality control chart techniques which was conducted from 1970 to 1980.
• Statistics and data analysis in geology, Shumway, R. H. (1987). This is a paper that helps define the field and also present new and essential methods in the qualitative analysis of geologic data.
• Using control charts to monitor process and product quality profiles, Woodall, W. H., Spitzner, D. J., Montgomery, D. C., & Gupta, S. (2004). Journal of Quality Technology, 36(3), 309-320. This paper discusses various issues that are involved in using control charts to monitor different process- and product-quality profiles as well as review the literature on the statistical process control on the topic. This application is related to functional data analysis.
• Multivariate control charts for individual observations, Tracy, N. D., Young, J. C., & Mason, R. L. (1992). Journal of quality technology, 24(2), 88-95. This paper provides a method which is based on the beta distribution to construct multivariate control limits at the start-up stage and uses an example derived from the chemical industry to illustrate that the procedure is an improvement over the approximate techniques.
• A review of multivariate control charts, Lowry, C. A., & Montgomery, D. C. (1995). IIE transactions, 27(6), 800-810. This is a review of the notes on control charts for multivariate quality control but with an emphasis on the developments which occurred since the mid-1980s. The use of principal components and regression adjustments of variables together with frequently used approximations in multivariate quality control are also discussed.
• The economic design of control charts: a unified approach, Lorenzen, T. J., & Vance, L. C. (1986). Technometrics, 28(1), 3-10. This article considers the choice of control parameters from an economic point of view and also a general process model from which the hourly cost function is derived.
• The Shewhart control chart—tests for special causes, Nelson, L. S. (1984). Journal of quality technology, 16(4), 237-239. This paper explains the tests collected for assignable causes to be applied to Shewhart control charts for means of normally distributed data and some comments that accompany these tests.
• Research issues and ideas in statistical process control, Woodall, W. H., & Montgomery, D. C. (1999). Journal of Quality Technology, 31(4), 376-386. This article gives an overview of current research on control charting methods for process monitoring and improvement and also includes a historical perspective together with ideas for future research.
• [Original content]Decomposition of T2 for Multivariate Control Chart Interpretation, Mason, R. L., Tracy, N. D., & Young, J. C. (1995). Journal of quality technology, 27(2), 99-108. This paper attempts to show that the interpretation of a signal from a T2 statistic is mostly aided when the corresponding value is divided into independent parts. This decomposition also provides information on which characteristic is significantly contributing to the signal.