If you've ever had to decide whether to report Cpk or Ppk, you're not alone. It's one of those questions that comes up constantly in quality engineering, and getting it wrong can lead to very different conclusions about your process. ## The Core Difference Cpk measures what your process *is capable of* when it's running in control. Ppk measures what your process *actually delivered* over a period of time. The formulas look almost identical. Same structure, different sigma estimate: - **Cpk** = min((USL - X̄) / 3σ_within, (X̄ - LSL) / 3σ_within) - **Ppk** = min((USL - X̄) / 3σ_total, (X̄ - LSL) / 3σ_total) Cpk uses the within-subgroup variation (short-term spread). Ppk uses total variation, which includes everything: shifts, drifts, operator changes, material lots, all of it. One denominator change. Completely different story. ## A Quick Example Say you've got a process that runs beautifully within each shift but drifts between shifts because of temperature swings. Within any given subgroup, the spread is tight. Over a full week, though, the overall spread is much wider. Cpk will look great here. It only sees the tight within-subgroup variation. Ppk will look worse because it captures that between-shift drift too. Neither number is wrong. They just answer different questions. | Index | What it tells you | |-------|-------------------| | Cpk | How capable is this process when it's stable? | | Ppk | How did this process actually perform over this time period? | ## When Cpk Makes Sense Use Cpk when your process is in statistical control (check with a control chart first), when you want to understand inherent capability, or when you're comparing machines or methods under controlled conditions. One thing to be strict about: your process has to actually be in control for Cpk to mean anything. Reporting Cpk on an unstable process will still give you a number. It just won't be a useful one. ## When Ppk Makes Sense Ppk is better when you want to describe actual performance over a real production period, when you're reporting to a customer what they received, or when your process may not be fully stable and you're being upfront about that. It's also the right choice for preliminary runs and PPAP submissions. Ppk tends to be more honest. It doesn't assume good behavior. It just measures what happened. ## Mistakes That Come Up a Lot **Reporting Cpk without checking stability.** This is the big one. If your control chart shows out-of-control signals, Cpk isn't valid. Always run a control chart before calculating capability. If the process isn't stable, report Ppk and note that stabilization is needed. **Ignoring the gap between Cpk and Ppk.** When Cpk is significantly higher than Ppk, that gap is a signal. Something is introducing variation between subgroups that doesn't show up within them. Shift changes, material lots, environmental drift, tool wear. That gap is basically a roadmap for improvement. Find the between-subgroup factors and reduce them. **Treating them as interchangeable.** Some organizations swap the terms freely. They shouldn't. If a customer asks for Ppk and you send Cpk, you may be overstating your process capability. **Too little data.** Both indices need enough data to be reliable. Aim for at least 25 subgroups for Cpk, and 100+ individual readings for Ppk. Less than that and your confidence intervals get wide enough to be useless. ## Cp and Pp (the Centered Versions) Cp and Pp ignore where your process mean sits relative to the spec limits. They only look at spread. - **Cp** = (USL - LSL) / 6σ_within - **Pp** = (USL - LSL) / 6σ_total If Cp is a lot higher than Cpk, your process has the spread to be capable but it's not centered. That's a targeting problem, and targeting problems are usually easier to fix than variation problems. ## How This Works in Practice 1. Collect data from your process (25+ subgroups) 2. Run a control chart (I-MR for individuals, X̄-R for subgroups) 3. Check for stability. No out-of-control signals. 4. If stable, report Cpk (and Cp for the centered comparison) 5. If not stable, report Ppk, note the instability, and investigate assignable causes 6. Compare Cpk to Ppk. A large gap means between-subgroup variation needs work. 7. Set targets. Most industries want Cpk ≥ 1.33 (4σ). Critical characteristics typically need ≥ 1.67 (5σ). ## Industry Thresholds | Cpk Value | Sigma Level | What It Means | |-----------|-------------|----------------| | < 1.00 | < 3σ | Not capable. Process is producing defects. | | 1.00 | 3σ | Marginally capable (2,700 ppm) | | 1.33 | 4σ | Capable. Typical minimum for production approval. | | 1.67 | 5σ | Highly capable. Required for safety-critical features. | | 2.00 | 6σ | World-class | ## Wrapping Up Cpk and Ppk aren't interchangeable and they aren't competing with each other. Use both, compare them, and let the gap between them point you toward what to fix next. And always: control chart first, then capability. Never the other way around.