Lesson 8: Process capability (Cp, Cpk, and knowing whether a process can meet spec)

This lesson closes out the Measure phase material. Once a measurement system is trustworthy, the next question is whether the process itself is actually capable of meeting the customer's requirement, expressed as a specification. Process capability analysis answers that question with numbers instead of impressions.

The prerequisite: a stable process

Process capability can only be calculated meaningfully on a process that is in a state of statistical control, meaning its variation is stable and predictable over time, with no unexplained shifts, trends, or unusual points. A process that is not stable does not have one consistent capability to measure; it has a moving target. This is why capability studies are always paired with a check for stability, typically a control chart, covered in Lesson 9 and expanded further at the Green Belt level, before any capability number is trusted. Calculating Cpk on an unstable process produces a number that looks precise and means very little.

Capability analysis: Cp and Cpk

Once stability is confirmed, capability compares the process's natural spread against the customer's specification limits, the Upper Specification Limit (USL) and Lower Specification Limit (LSL). Two indices are commonly used:

• Cp compares how wide the specification window is against how wide the process actually spreads, using six standard deviations as the process spread. It answers "could this process fit inside the spec, if it were perfectly centered," but it ignores where the process is actually centered.
• Cpk answers the more useful, real-world question: how capable is this process right now, including wherever it is actually centered. Cpk looks at the distance from the process mean to the nearer of the two specification limits, so a process that is perfectly narrow but badly off-center gets a poor Cpk score even though its Cp might look excellent.

A process can have a good Cp and a poor Cpk at the same time. That combination is a specific, useful diagnosis: the process is not too variable, it is simply aimed at the wrong target, which is usually a cheaper and faster problem to fix than reducing variation would be. A process with a poor Cp has the opposite problem: even perfectly centered, it is too inconsistent to reliably fit inside the specification, which typically requires a deeper Analyze-phase investigation into root causes of variation rather than a simple re-centering adjustment.

Attribute and discrete capability

Cp and Cpk are built for continuous, variable data measured against numeric specification limits. For attribute or discrete data, pass or fail, defective or not defective, there is no continuous spread to compare against a spec width in the same way. Capability for this kind of data is instead expressed directly in terms of the defect rate itself: percent defective, DPU, or DPMO, the metrics covered back in Lesson 2, translated if needed into an equivalent sigma level. A process is described as capable in attribute terms when its defect rate meets the target the customer or the business has set, rather than by a Cp or Cpk number.

Monitoring techniques

A capability study is a snapshot, not a guarantee. A process confirmed capable today can drift out of capability later if nothing keeps watching it, which is exactly the failure mode the Control phase, and specifically the control charts covered starting in the next lesson, exist to prevent. Ongoing monitoring compares new data against the capability baseline established during the study, and flags the process for investigation the moment its behavior starts to look different from the state it was originally measured in, rather than waiting for a customer complaint or a failed batch to reveal the drift after the fact.

A worked Cp/Cpk example, and Pp/Ppk

Suppose a spec calls for a part dimension between a Lower Specification Limit of 9.50 and an Upper Specification Limit of 10.50 (LSL = 9.50, USL = 10.50), and a stable process is measured with a mean of 10.10 and a standard deviation (σ) of 0.15. Cp = (USL - LSL) / 6σ = (10.50 - 9.50) / (6 × 0.15) = 1.00 / 0.90 = 1.11. Cpk = the smaller of (USL - mean) / 3σ and (mean - LSL) / 3σ = the smaller of (10.50 - 10.10) / 0.45 = 0.89 and (10.10 - 9.50) / 0.45 = 1.33, so Cpk = 0.89. Cp (1.11) looks acceptable, but Cpk (0.89) is noticeably lower, telling the team the process spread itself is fine but it is running closer to the upper limit than it should.

A related pair of indices, Pp and Ppk, are calculated with the exact same formulas as Cp and Cpk but use the overall, long-term sample standard deviation of all the collected data rather than the short-term, within-subgroup sigma that Cp and Cpk assume. Cp and Cpk describe a process's potential capability assuming it stays as stable as it was when sampled; Pp and Ppk describe its actual, overall performance capability, including any shifts or drift that crept in between subgroups over the full study period. When a process is genuinely stable, Cp and Pp, and Cpk and Ppk, come out close to each other; a noticeable gap between them is itself a sign that the process is not as stable as it first appeared.