Lean Manufacturing and Six Sigma Definitions

Glossary terms, history, people and definitions about Lean and Six Sigma

Westgard Rules

The Westgard rules are used for laboratory quality control using “runs” consisting of measurements of multiple samples (typically 2-4 samples), called multi-rule. They are based on the Western Electric Rules and Nelson Rules, but are modified for multiple samples in a laboratory setting.

The rules were originally developed by James Westgard. The rules are applied to the Levey-Jennings Chart instead of the traditional Shewhart individuals control chart, which uses slightly different calculations for the control limits.

Short hand notations are used to abbreviate different decision criteria or control rules, such as 12s to indicate 1 control measurement exceeding 2s control limits. The table below shows the notation using subscripts.


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A decision tree (below) is used to determine if the multiple samples collected when control was done can be released.

For this example, 2 samples are collected (N=2). These could be 2 measurements on one control material or 1 measurement on each of two different control materials.

The first decision is whether the samples pass the 12s rule. This test is in yellow, to be used as a warning to trigger application of the other rules. Anytime a single measurement exceeds a 2s control limit, you respond by inspecting the control data using the other rules (shown in white underneath). If both samples are within 2 standard deviations (2s), then the process is deemed “in-control” and the run is accepted.

If one or more samples are outside of 2 standard deviations, then the other rules are evaluated. If any one of the following rules are violated (13s, 22s, R4s, 41s or 10x-bar), then the process is deemed “out-of-control” and the run is rejected.

If none of the rules are violated, then the process is deemed “in-control” and the run is accepted.

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