Cpk vs. Ppk: Which Capability Index to Report and Why the Gap Between Them Matters
Your customer asks for a capability study and you calculate Cpk = 1.45 and Ppk = 1.12 for the same characteristic. Which number goes on the PPAP submission? And what does the gap between them tell you about your process? The difference between Cpk and Ppk is one of the most frequently misunderstood concepts in process capability analysis — and reporting the wrong index can create problems during audits or lead you to miss a real process stability issue.
Cpk vs. Ppk: The Core Difference in One Sentence
Cpk measures what your process is capable of producing when it is running in statistical control (short-term, within-subgroup variation only). Ppk measures what your process actually produced over a longer period (total observed variation, including between-subgroup shifts and drifts).
The distinction comes down to how each index estimates process spread:
| Index | Variation Used | Standard Deviation Estimate | Time Frame | Answers the Question |
|---|---|---|---|---|
| Cpk | Within-subgroup only | σwithin = R-bar / d2 | Short-term (inherent capability) | “What CAN this process do when stable?” |
| Ppk | Overall (total) | σoverall = √[∑(xi - x-bar)² / (n-1)] | Long-term (actual performance) | “What DID this process actually produce?” |
Both use the same formula structure: min[(USL − mean) / 3σ, (mean − LSL) / 3σ]. The only difference is which σ gets plugged in. This means Cpk ≥ Ppk always, because within-subgroup variation is always less than or equal to total variation. When the two values are nearly equal, your process is stable. When there is a significant gap, your process shifts or drifts over time even if each individual subgroup looks fine.
The Formulas Side by Side
Cp and Cpk (Potential Capability)
- Cp = (USL − LSL) / 6σwithin
- Cpk = min[(USL − X-double-bar) / 3σwithin, (X-double-bar − LSL) / 3σwithin]
- Where σwithin = R-bar / d2 (from your X-bar R chart control limit calculation)
Cp measures potential spread (process width vs. tolerance width) without considering centering. Cpk adjusts for how well the process is centered between specification limits. A process with Cp = 2.0 but Cpk = 0.8 has plenty of room in theory but is running too close to one specification limit.
Pp and Ppk (Observed Performance)
- Pp = (USL − LSL) / 6σoverall
- Ppk = min[(USL − X-bar) / 3σoverall, (X-bar − LSL) / 3σoverall]
- Where σoverall = the standard deviation of all individual measurements
Worked Example: What the Cpk–Ppk Gap Reveals
Consider a machining process for a bore diameter with specification 50.00 ± 0.10 mm (USL = 50.10, LSL = 49.90). You collect 30 subgroups of n=5 over three weeks:
| Parameter | Value |
|---|---|
| Grand mean (X-double-bar) | 50.02 mm |
| R-bar | 0.030 mm |
| σwithin = R-bar / d2 = 0.030 / 2.326 | 0.0129 mm |
| σoverall (from all 150 individual measurements) | 0.0195 mm |
Cpk Calculation
- Cpk = min[(50.10 − 50.02) / (3 × 0.0129), (50.02 − 49.90) / (3 × 0.0129)]
- Cpk = min[0.08 / 0.0387, 0.12 / 0.0387]
- Cpk = min[2.07, 3.10] = 2.07
Ppk Calculation
- Ppk = min[(50.10 − 50.02) / (3 × 0.0195), (50.02 − 49.90) / (3 × 0.0195)]
- Ppk = min[0.08 / 0.0585, 0.12 / 0.0585]
- Ppk = min[1.37, 2.05] = 1.37
Interpreting the Gap
Cpk = 2.07 says: “Within any given hour, this process is excellent — very little variation.” Ppk = 1.37 says: “Over three weeks, additional variation crept in that the within-subgroup estimate missed.”
The gap (σoverall / σwithin = 0.0195 / 0.0129 = 1.51) tells you that between-subgroup variation is roughly 50% larger than within-subgroup variation. Something is shifting between subgroups — material lot changes, thermal drift across shifts, tool replacement schedules, or fixture wear. Your control chart may be in control (no individual rule violations), but the process mean is wandering enough over time to inflate overall variation.
This is actionable information. If you can identify and eliminate the between-subgroup variation source, Ppk will converge toward Cpk and your actual defect rate will drop accordingly.
Which Index to Report and When
| Situation | Report | Why |
|---|---|---|
| PPAP initial submission (automotive) | Both Cpk and Ppk | AIAG PPAP manual requires Ppk ≥ 1.67 for initial process study. Some OEMs ask for both indices to assess stability. |
| Ongoing production monitoring | Cpk | Once the process is qualified and in statistical control, Cpk tracks inherent capability. Ppk is recalculated periodically (quarterly or annually) as a stability check. |
| Customer audit / quality review | Both, with control chart | Auditors want to see the process is both capable (Cpk) and stable over time (Ppk close to Cpk). A large gap raises questions about process control. |
| Short pre-production run (<25 subgroups) | Ppk only | You cannot reliably establish statistical control with limited data, so Cpk is premature. Ppk gives a conservative performance estimate. |
| Process improvement project (DMAIC) | Both, before and after | Cpk shows whether inherent variation improved. Ppk shows whether total performance improved. An improvement that raises Cpk but not Ppk means you fixed within-subgroup variation but not the between-subgroup drift. |
The AIAG SPC Reference Manual specifies Ppk ≥ 1.67 for initial process studies in automotive. For ongoing production, IATF 16949 expects Cpk ≥ 1.33 as a minimum for key characteristics, with many OEMs requiring ≥ 1.67. Aerospace programs under AS9100 typically require Cpk ≥ 1.67 for critical dimensions.
Common Capability Index Mistakes
- Reporting Cpk without verifying statistical control. Cpk assumes the process is stable. If your control chart shows out-of-control signals, Cpk is misleading — the process may not sustain that capability level. Fix the control chart first.
- Using Ppk on a short run and calling it capability. Ppk from 10 parts is not a capability study — it is a snapshot. The ASQ recommendation is a minimum of 100 individual measurements (e.g., 25 subgroups of n=4 or 20 subgroups of n=5) for a reliable capability estimate.
- Ignoring the Cpk–Ppk gap. If Cpk = 1.8 and Ppk = 1.1, your process looks great in short windows but delivers mediocre results overall. Investigating the gap is often more valuable than trying to reduce within-subgroup variation further.
- Confusing Cp with Cpk. Cp ignores centering. A process centered exactly on a specification limit can have Cp = 1.5 (plenty of spread room) but Cpk = 0 (half the output is out of spec). Always report Cpk, not Cp alone.
- Assuming normality without checking. Cpk and Ppk calculations assume normally distributed data. For non-normal processes (surface finish, positional tolerances, hardness values), the standard formulas overestimate or underestimate capability. Consider a Box-Cox or Johnson transformation before interpreting the index, or use a non-parametric method.
Need to calculate Cpk and Ppk from your measurement data? The SPC control chart tool generates both indices alongside your control chart so you can assess capability and stability in one view.