c-chart

{{Lowercase}}

{{Infobox control chart

| name = c-chart

| proposer = Walter A. Shewhart

| subgroupsize = n > 1

| measurementtype = Number of nonconformances in a sample

| qualitycharacteristictype = Attributes data

| distribution = Poisson distribution

| sizeofshift = ≥ 1.5σ

| meanchart = C control chart.svg

| meancenter = $\backslash bar\; c\; =\; \backslash frac\; \{\backslash sum\_\{i=1\}^m\; \backslash sum\_\{j=1\}^n\; \backslash mbox\{no.\; of\; defects\; for\; \}\; x\_\{ij\}\}\{m\}$

| meanlimits = $\backslash bar\; c\; \backslash pm\; 3\backslash sqrt\{\backslash bar\; c\}$

| meanstatistic = $\backslash bar\; c\_i\; =\; \backslash sum\_\{j=1\}^n\; \backslash mbox\{no.\; of\; defects\; for\; \}\; x\_\{ij\}$

}}

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.{{cite web|url=http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc331.htm|title=Counts Control Charts|accessdate=2008-08-23|work=NIST/Sematech Engineering Statistics Handbook|publisher=National Institute of Standards and Technology}} 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:{{cite book | last = Montgomery | first = Douglas | title = Introduction to Statistical Quality Control | publisher = John Wiley & Sons, Inc. | year = 2005 | location = Hoboken, New Jersey | pages = 289 | url = http://www.eas.asu.edu/~masmlab/montgomery/ | isbn = 978-0-471-65631-9 | oclc = 56729567 | access-date = 2008-08-23 | archive-url = https://web.archive.org/web/20080620095346/http://www.eas.asu.edu/~masmlab/montgomery/ | archive-date = 2008-06-20 | url-status = dead }}

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