Taylor state: Difference between revisions

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{{Lowercase}}
{{Infobox control chart
| name =            c-chart
| proposer =        [[Walter A. Shewhart]]
| subgroupsize =    n > 1
| measurementtype = Number of nonconformances in a sample
| qualitycharacteristictype = [[Variable and attribute (research)|Attributes data]]
| distribution =    [[Poisson distribution]]
| sizeofshift =    ≥ 1.5σ
| meanchart =      C control chart.svg
| meancenter =      <math>\bar c = \frac {\sum_{i=1}^m \sum_{j=1}^n \mbox{no. of defects for } x_{ij}}{m}</math>
| meanlimits =      <math>\bar c \pm 3\sqrt{\bar c}</math>
| meanstatistic =  <math>\bar c_i = \sum_{j=1}^n \mbox{no. of defects for } x_{ij}</math>
}}


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.


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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.  
 
Nonconformities may also be tracked by type or location which can prove helpful in tracking down [[assignable cause]]s.  
 
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:<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>
*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 <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.
 
==See also==
*[[u-chart]]
 
==References==
{{reflist}}
 
{{DEFAULTSORT:C-Chart}}
[[Category:Quality control tools]]
[[Category:Statistical charts and diagrams]]

Latest revision as of 11:47, 4 August 2013

Template:Lowercase Template:Infobox control 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.

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 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 c¯±3c¯ where c¯ is the estimate of the long-term process mean established during control-chart setup.

See also

References

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  1. ↑ Template:Cite web
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