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.