How is Cpk Calculated on Single Sided Dimensions
Cpk formulas used by QC-CALC
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written: 02/23/2007
last modified: 03/22/2024

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 using the n-1 method. This formula corresponds to Excel’s "STDEV()" function.

There are 3 methods of calculating Standard Deviation, also known as sigma (σ):




σ by N-1

Sigma Overall

σ by R

Sigma_by_R or Sigma Within

Uses the range within the subgroup

σ by S


Uses the Sigma within the subgroup

Cpku based on upper tolerance = (USL - Xbar) / 3σ

CpkL based on lower tolerance = (Xbar - LSL) / 3σ

Cpk = Lesser { Cpku, CpkL } Both Cpk and Ppk are calculated the same way (above equations) and differ only in the Sigma value they use. Ppk uses Sigma OverallCpk uses Sigma Within (Sigma By R).

For single-sided features QC-CALC only calculates the toleranced sided of the feature. For example, since a flatness only has a plus tolerance so QC-CALC calculates and uses the Cpku for Cpk. So for all single-sided upper toleranced features such as True Position, Concentricity, Flatness, Parallelism, Perpendicularity, Roundness, etc. QC-CALC uses Cpku for Cpk.