Nelson Rules (and Western Electric Rules) for Control Charts

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Control charts are an essential tool in statistical process control (SPC), allowing organizations to monitor and control the quality and stability of their processes. While control charts can help identify process variations and potential issues, interpreting the data can sometimes be challenging. Nelson rules, developed by Lloyd S. Nelson in the 1980s, provide a systematic approach to interpreting control charts by identifying specific patterns that may indicate process instability or other issues. This post will discuss the Nelson rules for control charts, their benefits, and how to apply them in your quality control efforts.

Nelson Rules: An Overview

There are eight Nelson rules that can be applied to control charts to identify potential issues and improve process monitoring. These rules are based on the assumption that data points within control limits and following a random pattern indicate a stable process. Any deviation from this random pattern may signal a problem.

Rule 1: One point is more than 3 standard deviations from the centerline. This indicates that an extreme variation has occurred, which is unlikely to happen in a stable process.

Rule 2: Nine or more consecutive points fall on the same side of the centerline. This suggests a persistent shift in the process, which could be due to a change in process inputs or other factors.

Rule 3: Six or more consecutive points are continually increasing or decreasing. This pattern may indicate a trend in the process, which could be the result of tool wear, material changes, or other causes.

Rule 4: Fourteen or more consecutive points alternate in direction (up and down). This pattern, called oscillation, could indicate instability in the process or a lack of control over process inputs.

Rule 5: Two out of three consecutive points fall more than 2 standard deviations from the centerline (on the same side). This pattern suggests a possible shift in the process mean or increased variability.

Rule 6: Four out of five consecutive points fall more than 1 standard deviation from the centerline (on the same side). This rule also suggests a possible shift in the process mean or increased variability.

Rule 7: Fifteen or more consecutive points fall within 1 standard deviation of the centerline (on either side). This pattern may indicate a reduction in process variation, which could result from an overly restrictive control or a change in process inputs. (The below example violates Rule 2 as well.)

Rule 8: Eight or more consecutive points fall outside 1 standard deviation from the centerline (on either side). This pattern suggests an increase in process variation, which could be due to changes in materials, tools, or other factors.

Western Electric Rules:

Developed by the Western Electric Company, these rules are designed to identify patterns in control charts that may indicate process instability or out-of-control conditions. The Western Electric rules consist of four primary rules:

Rule 1: One point is more than 3 standard deviations from the centerline.

Rule 2: Two out of three consecutive points are more than 2 standard deviations from the centerline (on the same side).

Rule 3: Four out of five consecutive points are more than 1 standard deviation from the centerline (on the same side).

Rule 4: Eight or more consecutive points are on the same side of the centerline.

Comparison Table (Nelson Rules vs Western Electric Rules):

Rule Number Rule Category Nelson Rule Description Western Electric Rule Description
1 Points beyond 3σ One point is more than 3 standard deviations from the centerline. One point is more than 3 standard deviations from the centerline.
2 Consecutive points on one side of the centerline Nine or more consecutive points fall on the same side of the centerline. Eight or more consecutive points are on the same side of the centerline.
3 Points beyond 2σ Two out of three consecutive points fall more than 2 standard deviations from the centerline (on the same side). Two out of three consecutive points are more than 2 standard deviations from the centerline (on the same side).
4 Points beyond 1σ Four out of five consecutive points fall more than 1 standard deviation from the centerline (on the same side). Four out of five consecutive points are more than 1 standard deviation from the centerline (on the same side).
5 Trending Six or more consecutive points are continually increasing or decreasing. -
6 Oscillation Fourteen or more consecutive points alternate in direction (up and down). -
7 Reduced Variation Fifteen or more consecutive points fall within 1 standard deviation of the centerline (on either side). -
8 Increased Variation Eight or more consecutive points fall outside 1 standard deviation from the centerline (on either side). -

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