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 = $ar{x} + 3sigma$ — upper boundary of expected variation. - **LCL**: Lower Control Limit = $ar{x} - 3sigma$ — 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.