Process capability calculator

Cp and Cpk from within-subgroup variation, Pp and Ppk from overall variation, computed side by side so the difference is visible. Companion to the three-wire, pre-plate, and TAR/TUR calculators.

Calculation aid. Not a stability assessment. Capability indices assume a process that is in statistical control and data that is approximately normal. This page checks normality and reports it, but it does not and cannot establish that a process is stable — that requires control charting over time, which is outside its scope. Indices computed on an unstable process describe the past, not what the process will deliver. All constants are computed from their definitions at run time; no table or worked example is reproduced from any published source. This page makes no determination of whether a capability figure satisfies a customer requirement or a standard. No warranty of any kind is made as to accuracy, completeness, or fitness for a particular purpose, and no liability is accepted for any loss or damage arising from its use. Version 1.0 · All constants computed, none transcribed · Last reviewed August 2026

Data and specification

Identification, optional

Part or characteristic

Record reference

Date

Printed with the results so the sheet can be attached to an inspection record. Not stored anywhere.

Measurement data Paste measurements

One value per line, or comma, tab, semicolon or space separated. Paste straight from a spreadsheet column. Readings are used in the order given, which matters for moving ranges and for subgrouping.

Subgrouping and specification

Subgroup size

Enter 1 for individuals. Sigma-within then comes from the moving range.

Units

Label only.

USL

Leave blank for a lower-only specification.

LSL

Leave blank for an upper-only specification.

Display decimals

Measurement error

Measurement variation, optional

Entered as

Value

In the same units as the measurement data. Leave blank if you do not want this section.

Formulas

d2(n), expected range of n standard normals	`∫ [ 1 − Φ(x)ⁿ − (1−Φ(x))ⁿ ] dx`
Sigma-within, subgrouped	`R̄ / d2(subgroup size)`
Sigma-within, individuals	`MR̄ / d2(2)`
Sigma-overall	`s`, sample standard deviation with n−1
c4(n), shown as an intermediate only	`√(2/(n−1)) · Γ(n/2)/Γ((n−1)/2)`
Cp, Pp both limits only	`(USL − LSL) / (6σ)`
CPU, PPU	`(USL − mean) / (3σ)`
CPL, PPL	`(mean − LSL) / (3σ)`
Cpk, Ppk	the smaller of whichever one-sided indices exist
Confidence interval	`Cpk ± z √( 1/(9n) + Cpk²/(2(n−1)) )`
Skewness, excess kurtosis	`g₁ = m₃/m₂^1.5` `g₂ = m₄/m₂² − 3`
Process sigma net of measurement	`√( σ_obs² − σ_meas² )`
Measurement-limited ceiling	`min(USL−mean, mean−LSL) / (3σ_meas)`

One-sided specifications. With only one limit entered, Cp and Pp are suppressed rather than filled with a substitute. A spread index has no meaning without a spread to compare against.

Not covered. Control charting and stability assessment. Non-normal capability methods and transformations. Anderson-Darling and other tests requiring published critical values. Confidence intervals on Cp, Pp or sigma. Attribute data. Multivariate capability. Autocorrelation.