How is Cpk calculated for single-sided tolerances
This white paper gives an overview of the single-sided calculation
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written: 02/07/2007
last modified: 02/14/2024


How is Cpk calculated for Single-Sided features such as flatness?


QC-CALC uses Cpku for Cpk for all single-sided upper tolerance features including Flatness, True Position, Concentricity, Parallelism, Perpendicularity, and Roundness.

QC-CALC does not calculate one side or the other on Single-Sided features. For example, a flatness only has a plus tolerance so QC-CALC calculates and uses the Cpku for Cpk. QC-CALC uses the only Cpk that is calculated for the particular side in use.

All calculations and reports in QC-CALC assume that your data set is a "sample" of the total parts, and not the entire set of data. For this reason, we always calculate "Sigma by N-1". This formula corresponds to Excel’s "STDEV()" function.

There are 3 methods of calculating Standard Deviation, also known as Sigma.

  • σ by N-1 (Sigma)
  • σ by S (Sigma_by_S)
  • σ by R (Sigma_by_R)

Cpku based on upper tolerance = cpku_upper_tol_formula.png

CpkL based on lower tolerance = cpku_lower_tol_formula.png

Cpk = Lesser { Cpku, CpkL }