Cp vs Cpk vs Pp vs Ppk: choose the right variation estimate

Capability indices compare process spread with engineering specifications. The distinction between Cp/Cpk and Pp/Ppk depends on the variation estimate, not on choosing a nicer result. Keep the time order and subgroup structure of the data so that a single index does not conceal drift or mixed production streams.

FIG. 03At the inspection gate

Width and centering answer different questions

For a two-sided specification, the width index is (USL − LSL) / (6 × sigma). The centered index is the smaller of (USL − mean) / (3 × sigma) and (mean − LSL) / (3 × sigma). The first compares widths; the second also accounts for the mean's distance from the nearer limit.

With LSL 9.5, USL 10.5, mean 10.1 and sigma 0.1, the width index is 1.6667 and the centered index is 1.3333. Moving the mean to 10.0 raises the centered index to 1.6667 without changing spread. Increasing sigma to 0.2 at mean 10.1 reduces the two indices to 0.8333 and 0.6667. Explore both changes with the capability calculator.

Label the sigma you actually used

In the convention used by Shopfloor's calculator, within-subgroup estimates produce Cp/Cpk; the overall sample standard deviation produces Pp/Ppk. An overall estimate can include shifts between subgroups that a short-term within estimate does not. Neither label rescues poor subgroup design.

The sample statistics calculator returns an overall sample standard deviation. Pasting that number into the within option would mislabel the calculation. Record the estimator, sampling plan, machine, cavity, product and time window with the result.

Specifications are not control limits

Specifications express what the product must meet. Control limits describe the observed behavior of a process under a chosen chart model. Using control limits as specifications makes capability circular: the process supplies both the output and the acceptance boundary.

Use a time plot and suitable SPC charts to examine stability first. Check measurement resolution and repeatability. A rounded list of identical readings can give zero sample spread even when the process is varying below the instrument's resolution.

Interpret with care

A mean outside the specification interval produces a negative centered index; keep that sign. There is no universal acceptance threshold for every characteristic and customer. Distribution shape, autocorrelation, sample size and mixed streams affect interpretation. A simple index is not a defect-rate estimate without further distribution assumptions, and a point estimate omits estimation uncertainty.

For an initial review, retain the raw observations, sampling plan, chart, specification revision and variation estimator. If the index affects product release, follow the approved quality procedure rather than treating a web result as a release decision.

Source and next step

NIST: process capability gives the two-sided formulas and statistical assumptions. The numeric examples are illustrative. Continue through the manufacturing performance learning path.