Analyzing and Interpreting a Control Chart

Basics of a Control Chart

• Axes:
  • Horizontal Axis: Time
  • Vertical Axis: Measure of Interest
• Centerline: Mean (X bar)
• Control Limits:
  • Upper Control Limit (UCL)
  • Lower Control Limit (LCL)

Zones and Sigma Limits

• Zones are labeled C, B, A from the centerline.
• Three Sigma limits are above and below the centerline.

Tests for Special Causes

• Common Cause Variation:
  • Data fluctuating between UCL and LCL is typically random and common.
• Special Cause Variation:
  • Exceeding Control Limits:
    • A data point beyond UCL or LCL indicates special cause.

Detecting Patterns

Shift and Trend

• Shift:
  • Occurs when several data points (usually 8 or more) hang above or below the centerline.
  • Indicates a consistent change in process level.
• Trend:
  • Occurs with 6 or more consecutive data points moving consistently up or down.
  • Suggests a gradual change in process.
  • Repetitions cancel trends.

Abnormal Patterns

• Two Out of Three Rule:
  • Two out of three consecutive data points in Zone A or beyond signal a special cause.
• 15 Data Points Hugging Centerline:
  • 15 consecutive data points close to the centerline (between Zone C's plus and minus 1 Sigma) indicate too little variation.
  • More than 68% of data within one standard deviation of the mean suggests abnormal pattern.

Summary of Rules

• Single Data Point Rule:
  • A single point exceeding UCL or LCL is a classic 3 Sigma violation.
• Other tests include shifts, trends, and patterns in the zones between control limits.

Conclusion

• Understanding these rules helps interpret the control chart effectively.
• Once the chart is built with mean, UCL, and LCL, applying these tests can diagnose the process's stability or identify special causes.