Control Limits

Control Limits are the statistically calculated boundaries on SPC control charts — typically set at ±3σ from the process mean, these limits define the expected range of natural process variation and are used to distinguish between common cause (in-control) and special cause (out-of-control) variation.

Control Limit Details

• UCL: Upper Control Limit = $\bar{x} + 3\sigma$ — upper boundary of expected variation.
• LCL: Lower Control Limit = $\bar{x} - 3\sigma$ — lower boundary of expected variation.
• 3σ Convention: ±3σ captures 99.73% of in-control data — false alarm rate of 0.27%.
• NOT Specification Limits: Control limits are based on process performance, NOT on product requirements.

Why It Matters

• Signal Detection: Points outside control limits signal special cause variation — investigate and correct.
• Process Voice: Control limits represent the "voice of the process" — what the process is naturally capable of.
• Rules: In addition to out-of-limit points, run rules (Western Electric rules) detect trends, shifts, and patterns.

Control Limits are the process guardrails — statistically derived boundaries that separate natural variation from assignable cause variation on SPC charts.