What is the difference between Cp and Cpk?

Cp compares the spec width to the process spread and ignores centering: it says whether the process could fit the spec if centered. Cpk measures from the actual mean to the nearest spec limit, so it reflects how the process really runs. Cpk is always less than or equal to Cp, and the gap between them measures how off-center the process is.

What is a good Cpk value?

By widespread convention, 1.33 (a 4 sigma margin to the nearest limit) is the minimum for ongoing production on important characteristics, and the AIAG PPAP manual's default criteria treat 1.67 or higher as acceptable for initial process studies. These are customer-driven conventions, not laws; some industries and characteristics demand more.

What is the difference between Cpk and Ppk?

Same formula, different standard deviation. Cpk uses short-term within-subgroup variation and describes what the process can do at its best; Ppk uses the overall standard deviation of all data, including drift and shift-to-shift wander, and describes what the customer actually experienced. Ppk is typically the lower number, and automotive practice commonly judges initial PPAP studies on Ppk.

Yes. Cpk goes negative when the process mean falls outside a specification limit, meaning more than half the output is out of spec on that side. Cp, by contrast, can never be negative, which is another reminder that Cp alone can look healthy while the process ships scrap.

How many parts do you need for a capability study?

Common practice is at least 100 individual values collected across 20-25 subgroups under normal running conditions, after the process has shown stability on a control chart. Smaller samples produce indices with wide uncertainty, so treat any Cpk computed from 30 parts as a rough estimate, not a verdict.

Does the process need to be in control before calculating Cpk?

Yes. Capability indices assume a stable process with one predictable spread and center. If a control chart shows special causes, the process has no single 'capability' to measure, and any index computed will change as soon as the next disturbance hits. Stabilize first, then measure.

What if there is only one specification limit?

Use the one-sided index: CPU = (USL − mean) ÷ 3σ for an upper limit only, or CPL = (mean − LSL) ÷ 3σ for a lower limit only, and report that as Cpk. Cp is undefined with a single limit because there is no spec width.

Cp and Cpk: Process Capability, Explained With Pictures

Process capability compares what a stable process actually produces against what the specification requires. Cp measures whether the process spread fits inside the spec limits; Cpk measures the same thing while accounting for how well the process is centered. Higher is better; a common conventional minimum is 1.33.

The indices get treated like mysterious report-card grades, but the picture behind them is simple: a bell curve sitting between two goalposts. Everything Cp and Cpk say can be seen by eye. This guide draws the pictures, works one example with real numbers, and is honest about where the famous 1.33 threshold comes from.

What is Cp?

Cp is the ratio of the spec width to the process spread: the distance between the specification limits divided by six standard deviations of the process. Cp = 1.0 means the process spread exactly fills the spec window. Cp = 2.0 means the spread uses half the window. Cp asks one question: could this process fit the spec if it were perfectly centered?

That "if" is Cp's blind spot. A process can have a beautiful Cp of 2.0 while running so far off center that half the parts are out of spec. Cp ignores where the process sits; it only measures how wide it is.

The fill-weight example, centered: the ±3σ spread fits with 4σ from the mean to each limit. Cp and Cpk agree at 1.33.

What is Cpk?

Cpk measures the distance from the process mean to the nearest spec limit, in units of three standard deviations. It answers the question Cp dodges: given where this process actually runs, how much room is there before the closest goalpost? When the process is perfectly centered, Cpk equals Cp. The moment the mean drifts, Cpk drops while Cp stays put. The gap between them is a direct reading of how off-center you are.

The same 2.5 g spread, mean drifted to 505 g. Cp still says 1.33; Cpk says 0.67 and about 2.3% of fills are over the limit.

A worked example: one filler, two verdicts

Take a filling line with a spec of 500 ± 10 grams, so LSL = 490 and USL = 510, a 20-gram window. Suppose a capability study on stable data shows a standard deviation of 2.5 grams.

Centered case: mean = 500 g. Spec width 20 g divided by six sigma (15 g) gives Cp = 1.33. The nearest limit is 10 g away, which is 10 ÷ (3 × 2.5) = Cpk = 1.33. Expected out-of-spec product: roughly 60 parts per million total, under normality.
Drifted case: the same machine creeps up to a mean of 505 g. The spread hasn't changed, so Cp is still 1.33. But the USL is now only 5 g away: 5 ÷ 7.5 = Cpk = 0.67 and about 2.3% of fills exceed 510 g. Same machine, same spread, twenty-thousand-fold more defects, and Cp never blinked.

That is the entire Cp-versus-Cpk story: report them together, and read the gap. A big gap says "center the process," which is usually cheap (an adjustment). A low Cp says "the spread itself is too wide," which is expensive (reduce variation or live with fallout). Knowing which problem you have before spending money is the practical value of computing both. The drift case is also why capability work rides on statistical process control: a control chart would have flagged that 5-gram creep long before the capability study did.

Cp is the process's potential; Cpk is its actual performance. Report both, read the gap.

What about Pp and Ppk?

Pp and Ppk use the same formulas with a different standard deviation. Cp/Cpk use short-term, within-subgroup variation, the process at its best behavior between disturbances. Pp/Ppk use the overall standard deviation of all the data, including drift, shift changes, and lot-to-lot wander. Ppk is therefore usually the lower, more honest number for "what did the customer actually experience," while Cpk describes the entitlement of the process if you eliminated the between-subgroup noise. Automotive practice reflects this split: initial studies at PPAP are commonly judged on Ppk, ongoing production on Cpk.

How do you run a capability study?

Confirm the measurement system first. If the gauge cannot repeat, the study measures the gauge, not the process.
Establish stability on a control chart. Capability math assumes a stable process. An out-of-control process has no single spread or center to measure, so any index computed from it is fiction.
Collect enough data under normal conditions. Common practice: at least 100 individual values across 20-25 subgroups, spanning routine sources of variation.
Check the distribution shape. The ppm predictions assume roughly normal data. Skewed data (flatness, runout, anything bounded at zero) needs transformation or different methods before the indices mean anything.
Compute Cp, Cpk (and Ppk), and read the pair. Low Cp: attack variation. Cp fine but Cpk low: center the process.
Re-check after any process change. Capability is a snapshot, not a property. Tooling wear, material changes, and new operators all move it, which is a running theme in first article inspection and requalification work.

Where does the 1.33 threshold actually come from?

Honestly: it is a convention, not a law of nature. Cpk = 1.33 means the process mean sits four standard deviations from the nearest spec limit (4σ ÷ 3σ = 1.33), which under normality predicts roughly 30 defective ppm on that side. It became the default because influential customers wrote it into supplier requirements, and it stuck.

The AIAG PPAP manual's default acceptance criteria for initial process studies treat an index of 1.67 or higher as acceptable, 1.33-1.67 as possibly acceptable with customer review, and below 1.33 as not meeting criteria (AIAG, Production Part Approval Process).
Cpk = 1.33 corresponds to a 4σ margin (~30 ppm one-sided under normality); Cpk = 1.67 corresponds to 5σ (~0.3 ppm); Cpk = 2.0 is the "six sigma" 6σ margin.
ASQ's process-capability resources carry the standard formulas and assumptions if you want the math straight from a standards body (ASQ, Process Capability).

Treat 1.33 as a floor for ongoing production on characteristics that matter, expect customers in automotive and aerospace to ask for more on new launches, and remember the number is only as good as the stability and measurement work under it.

Why capability numbers go stale

The most common capability failure isn't a bad study; it's a good study that nobody repeats. The index gets computed at launch, framed in a PPAP binder, and quoted for years while tooling wears and the mean wanders. If check weights and dimensional data are captured digitally at the station rather than on clipboards, capability stops being an annual archaeology project: the data for a fresh Cpk is already sitting in the system, next to the downtime log and the scrap reasons. That continuous view of quality data is exactly what Harmony's quality intelligence and paperwork digitization modules exist to provide alongside your QMS software and it is the difference between capability as a certificate and capability as a live number. Poor capability, left unmeasured, doesn't disappear; it just gets paid for in scrap, sorting, and complaints, the failure half of your cost of quality.