lower control limit

**LCL** (Lower Control Limit) is the **lower boundary on an SPC control chart, set at the process mean minus three standard deviations** — $LCL = ar{x} - 3sigma$ (for an X-bar chart), defining the lower edge of expected natural process variation. **LCL Details** - **X-bar Chart**: $LCL = ar{ar{x}} - A_2 ar{R}$ — mirrors the UCL calculation. - **R Chart**: $LCL = D_3 ar{R}$ — often zero for small subgroup sizes (n ≤ 6). - **Natural Boundary**: If the calculated LCL is below a natural boundary (e.g., zero for defect counts), set LCL at the boundary. - **Symmetric**: For normally distributed data, LCL and UCL are symmetric around the mean. **Why It Matters** - **Low-Side Alert**: Points below LCL may indicate process improvement (desirable) or measurement error — investigate either way. - **One-Sided**: Some parameters only have one meaningful limit (e.g., defect count only has UCL — lower is always better). - **Balance**: Both UCL and LCL violations require investigation — any out-of-control condition needs understanding. **LCL** is **the floor of normal** — the lower boundary of expected variation below which a special cause investigation is triggered.