Cpk vs. Ppk: What the Difference Actually Means on the Shop Floor

You run a capability study. The report comes back with four numbers: Cp, Cpk, Pp, and Ppk. Three of them look fine. One doesn’t. Your customer wants Ppk ≥ 1.67 for PPAP submission, and yours is 1.12.

Before you start adjusting tooling or arguing with your process engineer, it helps to understand what Ppk is actually measuring — and why it’s different from Cpk, which is sitting at a comfortable 1.54 in the same report.

This article explains the difference, when each index applies, and what a gap between them tells you about your process.

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The short version

Cpk measures how capable your process is right now, under controlled conditions, using only the variation that occurs within rational subgroups.

Ppk measures how your process has actually performed over time, using all the variation in the data — including the shifts and drifts between subgroups.

Same data. Different sigma estimate. Different question.

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What a rational subgroup is, and why it matters

A rational subgroup is a small batch of parts produced under essentially the same conditions — same operator, same setup, same short window of time. If you measure five consecutive parts off a press every hour, each set of five is a rational subgroup.

The point of rational subgroups is to capture within-subgroup variation: the noise inherent to the process when nothing has changed. Variation between subgroups — the hour-to-hour drift, the shift changeover, the tool wear — is treated separately.

Cpk uses only the within-subgroup variation to estimate sigma. The standard method is R-bar/d2: take the average range across all your subgroups, divide by a constant (d2) that depends on subgroup size, and that’s your sigma estimate. This is the Shewhart approach, codified in the AIAG SPC Reference Manual (2nd ed.) and ANSI/ASQ B1-1996.

Ppk ignores the subgroup structure entirely. It takes every individual measurement in the study and computes the overall sample standard deviation (the familiar n-1 formula). That sigma captures everything: within-subgroup noise and all the between-subgroup shifts that happened during the study.

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The formulas, side by side

For a process with upper spec limit (USL), lower spec limit (LSL), and process mean (x̄):

Cpk = min[ (USL − x̄) / (3 × σ̂_within), (x̄ − LSL) / (3 × σ̂_within) ]

Ppk = min[ (USL − x̄) / (3 × σ_overall), (x̄ − LSL) / (3 × σ_overall) ]

The only difference is the denominator. σ̂_within comes from R-bar/d2. σ_overall comes from the sample standard deviation of all measurements.

Cp and Pp follow the same pattern but use the full spec width instead of the distance to the nearest limit:

Cp = (USL − LSL) / (6 × σ̂_within)

Pp = (USL − LSL) / (6 × σ_overall)

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A concrete example

A 90-person contract manufacturer makes precision aluminum brackets for an automotive Tier 1. A critical hole diameter has a spec of 12.00 ± 0.05 mm (LSL = 11.95, USL = 12.05). They run a 30-subgroup capability study, five parts per subgroup, measuring one subgroup per hour across a full shift.

The study comes back:

Index	Value
Cp	1.72
Cpk	1.54
Pp	1.18
Ppk	1.06

Cpk looks fine. Ppk does not.

What happened? The within-subgroup variation is tight — the machine holds tolerance well over any given five-part run. But the overall sigma is much larger, because the process mean drifted across the shift. The first few subgroups ran slightly low; the last few ran slightly high. Each individual subgroup looked stable. The overall picture didn’t.

Ppk caught the drift. Cpk missed it, because Cpk’s sigma estimate is built from within-subgroup ranges and those ranges were small.

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When each index applies

Use Cpk when:

• Your process is in statistical control (the control chart shows no special causes)
• You want to characterize the process’s potential — what it could do if it stayed at its current center
• You’re evaluating a stable, mature process in ongoing production

Use Ppk when:

• You’re running an initial process study (pre-production, PPAP, first article)
• You don’t yet know whether the process is stable
• You want to characterize actual performance over the study period, including any drift or shifts that occurred
• Your customer or standard requires it (AIAG PPAP 4th edition uses Ppk as the default submission metric)

The AIAG PPAP manual sets the bar at Ppk ≥ 1.67 for acceptable initial capability, with 1.33–1.67 classified as “may be acceptable” pending customer review, and below 1.33 as not currently capable. Ford’s PPAP requirements specify Ppk > 1.67 for Phase 3 submissions. These thresholds apply to Ppk — not Cpk — because PPAP is an initial study, and the process’s long-term stability hasn’t been established yet.

Once a process is in production and demonstrably stable, ongoing monitoring typically shifts to Cpk, which is more sensitive to the process’s actual capability under controlled conditions.

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What the gap between Cpk and Ppk tells you

If Cpk and Ppk are close to each other, your process is stable. The within-subgroup variation and the overall variation are roughly the same, which means nothing significant is shifting between subgroups.

If Cpk is noticeably higher than Ppk, your process has between-subgroup variation that isn’t showing up in the within-subgroup ranges. Common causes:

• Mean drift over time — tool wear, thermal expansion, material lot changes
• Setup-to-setup variation — the process centers differently after each changeover
• Operator-to-operator differences — if multiple operators ran parts during the study
• Shift-to-shift effects — ambient conditions, different raw material batches

The gap is a diagnostic. A Cpk of 1.54 and a Ppk of 1.06 tells you the machine is precise but not consistent. The fix is not to tighten the machine — it’s to find and reduce the source of between-subgroup drift.

A Cpk of 1.20 and a Ppk of 1.18 tells you something different: the process is stable, but it doesn’t have much margin. The fix is to either center the process better (if it’s off-nominal) or reduce the fundamental variation.

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One-sided specs

Some characteristics only have one spec limit — a minimum tensile strength, a maximum surface roughness. When LSL or USL is absent, Cp and Pp are undefined (you can’t compute a ratio over the full spec width). Cpk and Ppk still work: you just use whichever of the two terms applies.

For a one-sided upper spec: Ppk = (USL − x̄) / (3 × σ_overall)

For a one-sided lower spec: Ppk = (x̄ − LSL) / (3 × σ_overall)

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A note on sample size

Both indices are estimates, and they’re sensitive to sample size. A 30-subgroup study with five parts per subgroup (150 measurements) gives you a reasonably stable estimate. A 10-subgroup study gives you a number with wide confidence intervals — the true Ppk could be meaningfully higher or lower than what you calculated.

The AIAG SPC manual recommends a minimum of 25 subgroups for a capability study. For initial PPAP submissions, 30 subgroups is the common practice. If your study is smaller than that, treat the indices as directional, not definitive.

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What to do today

If you’re looking at a capability report and the Cpk/Ppk gap is bothering you:

1. Check the control chart first. If the X-bar chart shows obvious drift or shifts, that’s your between-subgroup variation. Identify what changed during the study — tool wear, material lot, operator, ambient temperature.

2. Calculate the ratio σ_overall / σ̂_within. If it’s greater than 1.2 or so, there’s meaningful between-subgroup variation worth investigating. If it’s close to 1.0, the process is stable and the gap is just sampling noise.

3. Don’t adjust the process based on Cpk alone when Ppk is the submission metric. A process that looks capable on Cpk but not on Ppk has a stability problem, not a precision problem. Fixing precision won’t help.

4. If Ppk is below threshold, identify the largest contributor to between-subgroup variation before making any process changes. Run the study again after addressing that contributor, and compare.

The indices are tools, not verdicts. A Ppk of 1.06 doesn’t mean the process is broken — it means the process has variation that isn’t captured in the within-subgroup ranges, and that variation is worth understanding before your next PPAP submission.