Shewhart Statistical Quality Control Chart

Industrial & Systems Engineering

How It Works

Statistical process control uses Shewhart X-bar control charts to distinguish between natural common-cause process variation and unnatural special-cause variation. The upper and lower control limits are placed at ±3 standard deviations from the center line according to the central limit theorem. Consecutive sample points remaining within the ±3σ boundaries confirm process statistical stability.

Governing Equation
UCL, LCL = x̄̄ ± 3 · [σ / √(n)]  |  C_pk = min[(USL - μ)/(3σ), (μ - LSL)/(3σ)]