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Statistical Quality Control Using Control Charts


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:

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

An Xbar (R) Quality Control Chart

An Xbar (S) Quality Control Chart

Displaying the WECO Zones on an X Control Chart

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

The following control charts are also used for variables:

  • Levey-Jennings control chart
  • Individual measurements chart
  • Moving range chart

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.

  • The multi-rules procedure is commonly used with Levey-Jennings chart. In the Levey-Jennings control chart shown here (the right-hand side image), with no points being outside 3s, the run is accepted.

Westgard Rules Applied to a Levey-Jennings Control Chart

An Individual Measurements Chart

A Moving Range Chart

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

An Example of np Quality Control Charts

An Example of u Quality Control Charts