https://en.formulasearchengine.com/w/api.php?action=feedcontributions&feedformat=atom&user=157.82.247.129formulasearchengine - User contributions [en]2026-08-15T19:23:46ZUser contributionsMediaWiki 1.47.0-wmf.7https://en.formulasearchengine.com/w/index.php?title=Taylor_state&diff=22751Taylor state2013-08-04T10:47:42Z<p>157.82.247.129: /* Derivation */</p>
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<div>{{Lowercase}}<br />
{{Infobox control chart<br />
| name = c-chart<br />
| proposer = [[Walter A. Shewhart]] <br />
| subgroupsize = n > 1<br />
| measurementtype = Number of nonconformances in a sample<br />
| qualitycharacteristictype = [[Variable and attribute (research)|Attributes data]]<br />
| distribution = [[Poisson distribution]]<br />
| sizeofshift = ≥ 1.5σ<br />
| meanchart = C control chart.svg<br />
| meancenter = <math>\bar c = \frac {\sum_{i=1}^m \sum_{j=1}^n \mbox{no. of defects for } x_{ij}}{m}</math><br />
| meanlimits = <math>\bar c \pm 3\sqrt{\bar c}</math><br />
| meanstatistic = <math>\bar c_i = \sum_{j=1}^n \mbox{no. of defects for } x_{ij}</math><br />
}}<br />
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In [[statistical process control|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.<ref>{{cite web|url=http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc331.htm|title=Counts Control Charts|accessdate=2008-08-23|work=[http://www.itl.nist.gov/div898/handbook/index.htm NIST/Sematech Engineering Statistics Handbook]|publisher=[[National Institute of Standards and Technology]]}}</ref> It is also occasionally used to monitor the total number of events occurring in a given unit of time.<br />
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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. <br />
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Nonconformities may also be tracked by type or location which can prove helpful in tracking down [[assignable cause]]s. <br />
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Examples of processes suitable for monitoring with a c-chart include:<br />
*Monitoring the number of voids per inspection unit in [[injection molding]] or [[casting]] processes<br />
*Monitoring the number of discrete components that must be re-[[soldered]] per [[printed circuit board]]<br />
*Monitoring the number of product returns per day<br />
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The [[Poisson distribution]] is the basis for the chart and requires the following assumptions:<ref>{{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}}</ref><br />
*The number of opportunities or potential locations for nonconformities is very large<br />
*The probability of nonconformity at any location is small and constant<br />
*The inspection procedure is same for each sample and is carried out consistently from sample to sample<br />
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The control limits for this chart type are <math>\bar c \pm 3\sqrt{\bar c}</math> where <math>\bar c</math> is the estimate of the long-term process mean established during control-chart setup.<br />
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==See also==<br />
*[[u-chart]]<br />
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==References==<br />
{{reflist}}<br />
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{{DEFAULTSORT:C-Chart}}<br />
[[Category:Quality control tools]]<br />
[[Category:Statistical charts and diagrams]]</div>157.82.247.129