Process Capability for Tribology Measurements

Evaluate short-term capability and overall performance against one- or two-sided engineering specifications for tribology and measurement data.

Process data and specifications

Capability analysis

Actual capability

—Cpk

Cp—

Pp—

Ppk—

Estimated nonconformance— ppm

Mean—

Within σ—

Overall s—

Data basis—

Upper capability Cpu: —

Lower capability Cpl: —

How to use

Choose Sample observations to enter ordered measurements, or Summary statistics when a justified mean, within standard deviation, and overall standard deviation are already available.
Enter at least one specification limit in the same unit as the measurements. Add the optional target to display it on the plot.
For sample mode, paste at least two measurements in acquisition order. For summary mode, enter positive within and overall standard deviations; sample count is optional.
Select Calculate to update the result, metrics, normal-model nonconformance estimate, and plot. Select Reset to restore the worked example.
Read Cpk for short-term capability and Ppk for overall performance. Cp and Pp appear only for two-sided specifications; a one-sided specification uses the available Cpu/Cpl and Ppu/Ppl side.
Correct red validation messages before using a result. Confirm process stability, measurement-system adequacy, and distribution shape independently.
Do not use these indices alone for unstable, autocorrelated, strongly non-normal, mixed-population, censored, or very small datasets, or as a substitute for product acceptance criteria.

Equations used

Cp = (USL − LSL)/(6σwithin)

Cpu = (USL − x̄)/(3σwithin); Cpl = (x̄ − LSL)/(3σwithin); Cpk = min(Cpu, Cpl)

Pp = (USL − LSL)/(6soverall)

Ppu = (USL − x̄)/(3soverall); Ppl = (x̄ − LSL)/(3soverall); Ppk = min(Ppu, Ppl)

Sample mode: x̄ = Σxᵢ/n; soverall = √[Σ(xᵢ − x̄)²/(n − 1)]; σwithin = MR̄/1.128, where MRᵢ = |xᵢ − xᵢ₋₁|.

The normal-distribution estimate: PPMlower = 10⁶ Φ((LSL − x̄)/soverall); PPMupper = 10⁶[1 − Φ((USL − x̄)/soverall)].

Here USL, LSL, target, xᵢ, x̄, σwithin, and soverall share the selected measurement unit; all capability indices are dimensionless. Higher-side distances are positive toward USL and lower-side distances are positive toward LSL. The sample within estimate uses consecutive moving ranges of size two and d₂ = 1.128.

Assumptions and limits: limits are engineering specifications, observations represent a stable process, and the PPM estimate assumes independent normal behavior. Cp and Pp need both limits. Confidence intervals are not shown because the correct method depends on subgroup design, estimator, and distribution. Capability does not establish stability, normality, or acceptance.

References: NIST/SEMATECH process capability guidance; ISO 22514-2:2017; process-capability formula reference.

Interpretation notes

Cpk/Ppk below zero means the process mean lies outside a supplied limit. Values near 1.00 place the nearest specification about three standard deviations from the mean. The commonly used 1.33 threshold is contextual, not universal; use customer, safety, control-plan, and sampling requirements.

Related tools: Gage R&R helps quantify measurement-system variation before capability analysis, and Friction Test Statistics summarizes repeated friction data.