What type of control chart would be used to monitor the number of defects per unit is?

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
Control limits
Plotted statistic

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:

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

See also[edit]

• u-chart

References[edit]

1. ^ "Counts Control Charts". NIST/Sematech Engineering Statistics Handbook. National Institute of Standards and Technology. Retrieved 2008-08-23.
2. ^ Montgomery, Douglas (2005). Introduction to Statistical Quality Control. Hoboken, New Jersey: John Wiley & Sons, Inc. p. 289. ISBN 978-0-471-65631-9. OCLC 56729567. Archived from the original on 2008-06-20. Retrieved 2008-08-23.

Attributes data arise when classifying or counting observations The Shewhart control chart plots quality characteristics that can be measured and expressed numerically. We measure weight, height, position, thickness, etc. If we cannot represent a particular quality characteristic numerically, or if it is impractical to do so, we then often resort to using a quality characteristic to sort or classify an item that is inspected into one of two "buckets".

An example of a common quality characteristic classification would be designating units as "conforming units" or "nonconforming units". Another quality characteristic criteria would be sorting units into "non defective" and "defective" categories. Quality characteristics of that type are called attributes.

Note that there is a difference between "nonconforming to an engineering specification" and "defective" -- a nonconforming unit may function just fine and be, in fact, not defective at all, while a part can be "in spec" and not fucntion as desired (i.e., be defective).

Examples of quality characteristics that are attributes are the number of failures in a production run, the proportion of malfunctioning wafers in a lot, the number of people eating in the cafeteria on a given day, etc.

Types of attribute control charts Control charts dealing with the number of defects or nonconformities are called c charts (for count).

Control charts dealing with the proportion or fraction of defective product are called  p charts (for proportion).

There is another chart which handles defects per unit, called the u chart (for unit). This applies when we wish to work with the average number of nonconformities per unit of product.

For additional references, see Woodall (1997) which reviews papers showing examples of attribute control charting, including examples from semiconductor manufacturing such as those examining the spatial depencence of defects.

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