Process Capability

Overview

Process capability analysis measures how well a process meets the customer's requirements. It compares the natural variation of the process to specification limits and expresses the result in a handful of indices. It is a core Measure and Control tool to produce an objective before/after picture.

Cp: Potential capability — compares the specification width (USL − LSL) with natural variation (6σ). Cp ignores the mean's location; it only says whether the process is theoretically narrow enough.

Cpk: Actual capability — additionally accounts for how far the mean sits from the nearer spec limit. Cpk is always ≤ Cp. Low Cpk with high Cp signals off-centering.

Pp and Ppk: Long-term versions of Cp and Cpk using overall sample variation instead of within-subgroup variation. Pp/Ppk is usually worse because it includes drift and special causes.

Specification limits (USL, LSL): Tolerance limits set by the customer or designer. Capability is a ratio between process behavior and these limits — no spec, no capability.

Normality assumption: Classic indices assume normal data. For skewed or multi-modal data, Box-Cox transformations or percentile-based nonparametric variants are used.

Rules of thumb: Cpk < 1.00 = not capable, 1.00–1.33 = marginal, 1.33–1.67 = good, > 1.67 = very good. Automotive expects 1.33 as minimum and 1.67 as target.

Approach

• Get specification limits from requirements, drawings, or customer contracts.
• Collect data — stable, representative, at least 30 values, ideally 100+.
• Check stability (control chart) — only a stable process gives meaningful indices.
• Check normality (histogram, probability plot, Shapiro-Wilk). If off, transform or use nonparametric method.
• Compute indices (Cp, Cpk, Pp, Ppk) and report with confidence intervals.
• Visualize — histogram with spec limits and fitted normal curve.
• Interpret: capable / not capable / shift vs. spread dominating.

Pitfalls

Capability on an unstable process: Indices from a drifting or disturbed process are worthless — they reflect the current snapshot, not the real behavior. Secure stability before any capability analysis.

Non-normal data ignored: A skewed distribution plugged into classical formulas yields wrong Cpk values — often worse than reality. Check the distribution first and transform if needed.

Too few data: At n = 15 the confidence interval for Cpk is so wide the result is meaningless. Use at least 30, preferably 100+ observations.

High Cp, low Cpk: The classic off-centered case: the process is narrow enough but shifted. The fix is not to reduce variation but to recenter the mean.

Reporting only Cp: Cp without Cpk hides off-centering. Always report both.

Self-set specifications: When the same company sets the spec and measures its own capability, the threshold tends to be chosen so that the number "fits". Specs come from the customer or function — not from the analyst.

Confusing Cp/Cpk with Pp/Ppk: Cp/Cpk uses short-term variation, Pp/Ppk long-term. Both are useful but not interchangeable — use the acronyms consistently and match them to the dataset.

Examples

This module ships with the following example datasets — load any of them in the app with a single click.

Available in the following cycles

• DMAIC: Measure
• DMADV: Measure
• 8D: D2 — Describe the Problem