c-chart

c-chart
Originally proposed by	Walter A. Shewhart
Process observations
Rational subgroup size	n > 1
Measurement type	Number of nonconformances in a sample
Quality characteristic type	Attributes data
Underlying distribution	Poisson distribution
Performance
Size of shift to detect	≥ 1.5σ
Process variation chart
Not applicable
Process mean chart
Center line	$\bar c = \frac {\sum_{i=1}^m \sum_{j=1}^n \mbox{no. of defects for } x_{ij}}{m}$
Control limits	$\bar c \pm 3\sqrt{\bar c}$
Plotted statistic	$\bar c_i = \sum_{j=1}^n \mbox{no. of defects for } x_{ij}$

In statistical quality control, the c-chart is a type of control chart used to monitor "count"-type data, typically total number of nonconformities per unit.^[1] It is also occasionally used to monitor the total number of events occurring in a given unit of time.

The c-chart differs from the p-chart in that it accounts for the possibility of more than one nonconformity per inspection unit, and that (unlike the p-chart and u-chart) it requires a fixed sample size. The p-chart models "pass"/"fail"-type inspection only, while the c-chart (and u-chart) give the ability to distinguish between (for example) 2 items which fail inspection because of one fault each and the same two items failing inspection with 5 faults each; in the former case, the p-chart will show two non-conformant items, while the c-chart will show 10 faults.

Nonconformities may also be tracked by type or location which can prove helpful in tracking down assignable causes.

Examples of processes suitable for monitoring with a c-chart include:

• Monitoring the number of voids per inspection unit in injection molding or casting processes
• Monitoring the number of discrete components that must be re-soldered per printed circuit board
• Monitoring the number of product returns per day

The Poisson distribution is the basis for the chart and requires the following assumptions:^[2]

• The number of opportunities or potential locations for nonconformities is very large
• The probability of nonconformity at any location is small and constant
• The inspection procedure is same for each sample and is carried out consistently from sample to sample

The control limits for this chart type are $\bar c \pm 3\sqrt{\bar c}$ where $\bar c$ is the estimate of the long-term process mean established during control-chart setup.

See also

• u-chart

References

1. "Counts Control Charts". NIST/Sematech Engineering Statistics Handbook. National Institute of Standards and Technology. Retrieved 2008-08-23.
2. Montgomery, Douglas (2005). Introduction to Statistical Quality Control. Hoboken, New Jersey: John Wiley & Sons, Inc. p. 289. ISBN 978-0-471-65631-9. OCLC 56729567.