CpCpk

Cp and Cpk are process capability indices used in quality engineering to quantify how well a manufacturing process can produce output within specified limits. They assess the relationship between the process distribution and the product specifications.

Cp is the potential capability of a process assuming it is perfectly centered within the specification limits. It is defined as Cp = (USL − LSL) / (6σ), where USL and LSL are the upper and lower specification limits and σ is the process standard deviation.

Cpk measures actual capability considering the process mean’s distance from the center of the specification, reflecting centering as well as spread. It is defined as Cpk = min[(USL − μ) / (3σ), (μ − LSL) / (3σ)], where μ is the process mean. The two terms compare how close the mean is to each limit relative to process spread; the smaller value governs Cpk.

Interpretation commonly uses the idea that higher values indicate a more capable and better-centered process. Rough benchmarks often cited are Cp or Cpk above 1.33 for a reasonably capable process, with higher values indicating greater capability, though targets depend on industry, product, and risk.

Estimation typically relies on sample data, with μ and σ estimated from measurements. Both indices assume a stable, approximately normal distribution of the process output and can be sensitive to outliers or non-normal behavior. Related long-term indices include Pp and Ppk, which use the overall variability across all data rather than short-term samples.