Cp / Cpk Process Capability
Turn spec limits and process spread into Cp, Cpk, and the sigma level that predicts your reject rate.
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The engineering
Cp asks whether the tolerance band is wide enough for the natural spread of the process — six sigma of scatter fit inside the spec width. Cpk adds the reality check of centering: it penalizes a process whose mean has drifted toward one limit, so Cp is always ≥ Cpk. Reach for this card whenever a control chart is stable and you need a single number to report capability.
Rule of thumb from AIAG-era automotive practice: Cpk ≥ 1.33 is the usual acceptance floor (4σ each side), and 1.67 is the target for critical characteristics. The gotcha is that these numbers only mean anything when the process is in statistical control and roughly normal — a bimodal or trending process makes both indices lie. And the ppm here is short-term about your actual mean, not the 1.5σ-shifted long-term figure some Six Sigma tables quote.
Where this math comes from
Capability indices grew out of Walter Shewhart's control-chart work at Bell Labs in the 1920s, but the specific Cp/Cpk shorthand came later. The idea of comparing tolerance width to process spread was formalized in Japanese manufacturing through the 1960s and 1970s, where the ratio of specification to six-sigma spread became a routine acceptance test on the shop floor.
The notation crystallized in the West when the Big Three automakers pushed statistical process control onto their supply base. The AIAG Statistical Process Control reference manual, first issued in 1991, pinned down Cp, Cpk, Pp, and Ppk definitions that suppliers still cite today, making the 1.33 minimum a contractual reality rather than a suggestion.
- 1924Walter ShewhartInvents the control chart, defining process spread as ±3σ.
- 1956Joseph JuranPopularizes the capability ratio comparing tolerance to process variation.
- 1986Victor KanePublishes the definitive 'Process Capability Indices' paper formalizing Cpk.
- 1991AIAGSPC reference manual standardizes Cp/Cpk definitions for automotive suppliers.
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