C-chart explained

c-chart
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:

\barc=

m
\sum
n
\sum
j=1
no.ofdefectsforxij
i=1
m
Meanlimits:

\barc\pm3\sqrt{\barc}

Meanstatistic:

\barci=

n
\sum
j=1

no.ofdefectsforxij

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:

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

The control limits for this chart type are

\barc\pm3\sqrt{\barc}

where

\barc

is the estimate of the long-term process mean established during control-chart setup.

See also

Notes and References

  1. Web site: Counts Control Charts. 2008-08-23. NIST/Sematech Engineering Statistics Handbook. National Institute of Standards and Technology.
  2. Book: Montgomery, Douglas . Introduction to Statistical Quality Control . John Wiley & Sons, Inc. . 2005 . . 289 . 978-0-471-65631-9 . 56729567 . 2008-08-23 . https://web.archive.org/web/20080620095346/http://www.eas.asu.edu/~masmlab/montgomery/ . 2008-06-20 . dead .