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Statistical Quality Control Using Control Charts
Shewhart Control Charts and Western Electric Company (WECO) Rules
Other Control Charts Used for Variables and Westgard Procedure Rules
Shewhart Control Charts for Attributes (p, np, c, and u Charts)
Introduction
Control charts are used to monitor a process for some quality characteristic such as e.g., thickness, weight, defective fractions, etc. The common elements of quality control charts are outlined below:
- The Y-axis (vertical axis)) is a value axis that is scaled according to the unit of the corresponding summary statistic (e.g., standard deviation, mean, etc.)
- The X-axis (horizontal axis) is categorical and represents sample ID, order, sequence, run time, site, etc.
- Each point represents a summary statistic based on computation results from subgroup measurements of a continuously varying quality characteristic.
- The center line displays the average of the summary statistic. The upper and lower control limit lines (UCL and LCL) display the range of expected variations in the summary statistic. Points above the UCL or below the LCL lines are out-of-control points, while points inside the UCL and LCL are in-control-points.
Shewhart Control Charts for Variables
These charts are based on quality characteristics that can be measured and expressed numerically.
- Xbar (R) chart/LI>
- Xbar (S) chart/LI>
- R chart
- S chart
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Special Cause Variation (WECO Rules)Western Electric Company (WECO) rules: The Shewhart Xbarcontrol chart that signals out-of-control conditions when a single point falls beyond +3 sigma or -3sigma is sensitive to detecting large shifts in the process average, but is rather insensitive to small shifts in the process average. Aabel's implementation of tests that make the Shewhart charts more sensitive to the latter shifts are those described in Western Electric Company (WECO) (1956) and Nelson (1984) procedure rules. The WECO rules can be used for Xbar (R), Xbar (S) and individual measurements charts, and require that groups/subgroups have equal sample sizes. |
Other Control Charts Used for Variables
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The following control charts are also used for variables:
Special Cause Variation (Westgard Procedure Rules)The Westgard multi-rules procedure, published by Westgard et. al. (1981), is used to detect trends or shifts by examining individual values to determine the status of the measuring system.
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Shewhart Control Charts for Attributes
The QC charts for attributes are based on quality characteristics that are attributes and expressed categorically, for example "conforming" or "non-conforming", "defective" or "non-defective", etc.
- p chart
- np chart
- c chart
- u chart
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