c-chart

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.

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	${\displaystyle {\bar {c}}={\frac {\sum _{i=1}^{m}\sum _{j=1}^{n}{\mbox{no. of defects for }}x_{ij}}{m}}}$
Control limits	${\displaystyle {\bar {c}}\pm 3{\sqrt {\bar {c}}}}$
Plotted statistic	${\displaystyle {\bar {c}}_{i}=\sum _{j=1}^{n}{\mbox{no. of defects for }}x_{ij}}$

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 ${\displaystyle {\bar {c}}\pm 3{\sqrt {\bar {c}}}}$ where ${\displaystyle {\bar {c}}}$ is the estimate of the long-term process mean established during control-chart setup.