Guide
What is the difference between Cpk and Ppk on machined parts?
Cpk is the process capability index that compares a dimension’s tolerance with the short-term, within-subgroup variation of a process that is in statistical control; Ppk is the process performance index that makes the same comparison using the total variation of every part measured. The whole Cpk vs Ppk question comes down to which standard deviation sits in the denominator, and that one choice decides what the number can and cannot promise about the next lot.
By Saola Manufacturing engineering team · Published · Updated
This guide is written for the supplier quality engineer or design engineer who has to request capability data on a few critical dimensions of a turned or milled part, and then judge what comes back. It covers the two formulas, how many parts each needs, the acceptance values most buyers borrow from the automotive PPAP manual, the ways machining data quietly inflates an index, and the exact wording to put on a drawing and an RFQ. Definitions follow the NIST/SEMATECH e-Handbook and the ISO 22514 series on capability and performance; acceptance values are those of the AIAG PPAP manual.
On this page
What do Cpk and Ppk each measure?
Both indices divide the distance from the process mean to the nearest specification limit by three standard deviations. Cpk uses the within-subgroup standard deviation, which describes how well the process can perform when only common-cause variation is present, while Ppk uses the overall standard deviation of all the data, which describes how the parts actually turned out.
Written out, Cpk is the smaller of (USL − mean) and (mean − LSL), divided by three times sigma-within. Sigma-within is estimated from the subgroups, most often as the average range divided by the d2 constant for the subgroup size, or as the pooled subgroup standard deviation. Ppk is the same expression with the ordinary sample standard deviation of every reading in the denominator. The NIST/SEMATECH e-Handbook sets out the Cp and Cpk definitions and the assumptions behind them: the characteristic is normally distributed and the process is in statistical control. Pp and Ppk follow the same normality assumption but drop the requirement for control.
Cp and Pp are the companion indices without the “k”. They divide the full tolerance width by six standard deviations and ignore where the mean sits, so they measure potential, not delivered, performance. A turned diameter with Cp of 2.0 and Cpk of 0.9 is a precise process aimed at the wrong size: an offset problem, not a machine problem. A Cpk close to Cp means the process is centered.
The practical reading of the pair is simple. Cpk answers “how good could this process be if nothing changed between subgroups?” Ppk answers “how good was it, over everything that did change?” On a machined feature the things that change between subgroups are tool wear, offset adjustments, thermal growth after a warm-up, a new bar or casting lot, and a change of operator or fixture. Ppk carries all of those; Cpk carries none of them.
Cpk vs Ppk: which number should you ask a supplier for?
Ask for Ppk from the initial production run when a part is being approved, and for Cpk from control-chart data once the process has shown it is stable. The gap between the two is itself the most useful diagnostic you will get.
Ppk suits a launch because a new process has not yet earned the assumption of stability that Cpk relies on. The AIAG PPAP manual asks for an initial process study on special characteristics and grades it with one set of acceptance values that it applies to whichever index the study reports: Cpk when the data show a stable process, Ppk otherwise. Many customer-specific requirements go further and ask for Ppk at launch outright. Once production is running and charted, Cpk from subgrouped data is the ongoing measure, because only a stable process can be predicted at all.
When a supplier sends both, compare them. If Ppk is close to Cpk, almost all the variation lives inside the subgroups and the process is stable. If Ppk is well below Cpk, something between subgroups is moving the mean, and on a CNC lathe or machining center that is usually tool wear and the sawtooth pattern of offset corrections, warm-up drift, or two spindles, pallets or fixtures being reported as one process. A Ppk slightly higher than Cpk is normal sampling noise in a stable process. A Ppk clearly higher than Cpk is a warning sign of a different kind: something is inflating the within-subgroup spread, usually subgroups that mix parts from different spindles, fixtures or times, or an operator adjusting the offset after nearly every part.
The table shows what a given index value means if the characteristic is normally distributed, and how the PPAP manual grades it. The nonconforming rates count only the tail beyond the nearest limit; a centered process with the same index has the same rate again beyond the other limit. They are only as good as the normality assumption.
| Cpk or Ppk | Distance to nearest limit (sigma) | Expected nonconforming (ppm, one tail) | PPAP grading of an initial-study index |
|---|---|---|---|
| 1.00 | 3 | 1350 | Does not meet acceptance |
| 1.33 | 4 | 32 | Lower bound of “may be acceptable” |
| 1.67 | 5 | 0.29 | Upper bound of “may be acceptable”; above it meets acceptance |
| 2.00 | 6 | 0.001 | Meets acceptance |
How many parts does a valid Cpk or Ppk need?
The PPAP convention for a preliminary study is at least 25 subgroups and at least 100 individual readings, taken from a significant production run. With only 30 or so readings, an index is so uncertain that a value of 1.33 cannot be told apart from 1.0.
Per the AIAG PPAP manual, the significant production run is 1 to 8 hours of production with at least 300 consecutive parts unless the customer states otherwise, and the study data come from that run. The usual subgroup on a machined part is a handful of consecutive parts off the same spindle and fixture, taken at intervals through the run, so that each subgroup sees only short-term variation and the intervals catch the drift. Subgroups need not be large; what matters is that the parts in each one were made back to back and that the subgroups span the conditions the process will meet in production.
The reason for the sample rule is the confidence interval. An index is an estimate, and the NIST/SEMATECH e-Handbook gives an approximate interval for Cpk that narrows only with the square root of the sample size. The second table applies that approximation to a reported value of 1.33. With 30 parts the true value could plausibly be anywhere from just under 1.0 to nearly 1.7, which is the whole range from “rejected” to “meets acceptance”. A Ppk calculated from a five-part first article tells you nothing about capability at all; a first article checks that every dimension can be made once, which is a different question.
Short runs need a different plan, not a smaller version of the same one. If the order is a few hundred parts, agree on a smaller run and a lower confidence, or ask for a full dimensional layout of several parts plus a control chart of the critical dimension through the run. For families of similar parts on the same machine, a capability study on the shared feature (one bore size, one thread) can carry over between part numbers if the customer agrees to it in writing.
| Readings in the study | Lower limit of Cpk | Upper limit of Cpk |
|---|---|---|
| 30 | 0.97 | 1.69 |
| 50 | 1.05 | 1.61 |
| 100 | 1.13 | 1.53 |
| 125 | 1.15 | 1.51 |
| 300 | 1.22 | 1.44 |
What Cpk and Ppk targets are typical in PPAP?
The common pattern is a Ppk above 1.67 at approval and a Cpk of at least 1.33 in ongoing production. Many OEMs raise or lower those values for particular characteristics in their own customer-specific requirements, and those override the manual.
The AIAG PPAP manual treats an initial-study index above 1.67 as meeting acceptance, 1.33 to 1.67 as possibly acceptable after review with the customer, and below 1.33 as not meeting acceptance, which usually triggers 100 percent inspection of that characteristic and a corrective action plan. Some customer-specific requirements set a single higher value, such as 1.67 for both Cpk and Ppk on safety characteristics, or a looser value on characteristics that are hard to measure or of low consequence.
Three situations break the simple targets. A one-sided requirement, such as a minimum thread depth or a maximum surface roughness, has only one limit, so only the upper or lower half of Cpk applies and Cp has no meaning. A geometric tolerance bounded at zero, such as position, flatness, runout or perpendicularity, produces skewed data that cannot go below zero, and a normal-theory index computed on it can badly misstate the real nonconforming rate; the index should come from a fitted non-normal distribution instead. And a dimension whose tolerance is close to the resolution of the gauge gives stepped data that no index describes well. In all three cases, ask for the histogram and the distribution model used, not only the number.
Set targets where they matter. A capability requirement on every dimension of a ballooned drawing multiplies inspection and paperwork without improving the part; most buyers flag the handful of characteristics that govern fit, sealing or safety, and leave the rest to the first article and lot inspection. The guide to the cost of tight tolerances explains why the same logic applies to the tolerances themselves.
What mistakes make capability numbers misleading on machined parts?
Most inflated indices on machined parts come from the measurement system, the way subgroups were formed, or a process that was not stable when the data were taken. None of these show up in the index itself, which is why the raw data matter more than the summary.
- An inadequate gauge. The traditional rule of ten is that the gauge should resolve about one tenth of the tolerance, and the AIAG MSA manual treats a gauge R&R under 10 percent as generally acceptable and over 30 percent as unacceptable, measured against the tolerance when the gauge is used to accept parts. Measurement error adds to the observed spread, so a poor gauge drags the index down; a gauge that rounds every reading to the same value does the opposite and makes the spread look artificially small.
- Subgroups that are not consecutive. Taking one part per hour and calling five of them a subgroup puts the drift inside the subgroup and makes Cpk and Ppk converge for the wrong reason.
- Mixed streams. Two spindles, a twin-pallet machining center or a multi-cavity fixture are separate processes. Pooled, their offsets look like spread; reported separately, each stream can be judged and corrected.
- Unstable data. If the control chart shows points outside the limits or a clear trend, Cpk does not describe anything. The NIST e-Handbook section on variables control charts covers the chart types that should come with the study.
- Data from the wrong moment. A study run on a warm machine with fresh inserts and the best operator describes the best hour of the process. Ask when in the tool life and shift the data were collected.
- Edited data. A capability index from a list of readings that contains no value outside a narrow band, or no repeated values at all, deserves a question. Sorted or cleaned data usually look too good.
What should the drawing and the RFQ say about capability?
Mark each critical characteristic on the drawing, then state in the RFQ which index you want, the target, the run and sample plan, and the data you expect to receive. A requirement written that way can be quoted and inspected; “Cpk 1.33 on all dimensions” cannot.
On the drawing, identify the characteristic with your company’s symbol for a key or critical characteristic and a note that defines it. A typical note reads: “Characteristics marked with the critical-characteristic symbol require Ppk of 1.67 or higher from the initial production run and Cpk of 1.33 or higher in ongoing production, calculated per ISO 22514-2 from subgroups of consecutive parts.” Keep the requirement on the drawing short and put the study details in the purchase specification, where they can change without a drawing revision.
In the RFQ or quality agreement, ask for:
- The list of capability characteristics, by balloon number, with the index and target for each.
- The run: how many parts, from which machine and fixture, and over what period.
- The subgroup plan: subgroup size, sampling interval and number of subgroups.
- The gauge for each characteristic and a gauge R&R study on it.
- The raw readings in a spreadsheet, in production order, with subgroup and machine identified.
- The control chart, the histogram, the distribution model used and, for zero-bounded GD&T characteristics, how non-normal data were handled.
- What happens below target: containment by 100 percent inspection, the reaction plan, and when the study is repeated.
Then read what comes back against the raw data, not the summary page. Recompute Ppk from the readings, check that Ppk does not exceed Cpk, look at the chart for trends and at the histogram for a second peak. The guide to PPAP for non-automotive parts covers how to fit a capability study into a smaller submission, and the AQL sampling guide covers lot acceptance for the dimensions that are not on the capability list.
How does Saola handle dimensions marked for capability control?
When a drawing marks a dimension as a process-capability control point, Saola treats it as one of the values watched through the run, not only at first article, and checks it more often than the rest of the print. The study itself, its sample plan and the index you want should be named on the RFQ so they are confirmed in the quote.
That practice is described on the quality and inspection page, which also lists what ships: a first-article inspection report covering every toleranced dimension on the drawing, and a dimensional inspection record with sample measurements from each production lot. The same page states what cannot be supplied yet: a signed ISO 9001 certificate, because certification is in progress, a third-party quality audit report, and a published PPM or on-time-delivery record. A formal capability study is not on the standard document list, so put the characteristics, target and sample plan from the previous section into the RFQ.
For turned features, the CNC turning page notes that every dimension called out to a tight tolerance adds inspection time, which is the same argument for limiting capability requirements to the characteristics that need them. Machined features on castings are covered on the CNC milling page, which notes that every GD&T callout is measured and logged. To have a part and its critical characteristics reviewed, send the drawing for a quote with the capability list attached.
Frequently asked
Can Ppk be higher than Cpk?
Only slightly, and a clear gap points to a problem. Overall variation includes within-subgroup variation, so Ppk is normally equal to or a little lower than Cpk, and in a stable process sampling noise can put it a little above. A clearly higher Ppk usually means each subgroup mixes parts from different spindles, fixtures or times, or the offset was adjusted after nearly every part.
Is a Cpk of 1.33 good enough?
For most ongoing production characteristics it is the common minimum, corresponding to four standard deviations between the mean and the nearest limit. Whether it is enough depends on the consequence of a bad part and on how many readings stand behind it: a 1.33 from 30 parts is far weaker evidence than a 1.33 from 300.
Can I get a meaningful Cpk on a small order?
Only with care. A short run rarely contains enough subgroups for a stable estimate, so agree on a reduced study in writing or replace it with a full layout of several parts and a run chart of the critical dimension. Capability data on a shared feature across a family of similar parts is another accepted route.
What is the difference between Cpk and Cpm?
Cpm penalizes distance from a target value rather than only distance from the limits, so a narrow process sitting off the target scores lower even when it is well inside the limits. It is useful when the nominal itself matters, for example a press-fit diameter, but it is far less common on drawings and purchase orders than Cpk and Ppk.
Should capability be measured on the machine or in the inspection room?
The study should use the gauge that will accept or reject the part in production, and that gauge needs its own R&R study. On-machine probing is fast but measures with the machine’s own errors included; if it is used, say so in the report.
Sources
- NIST/SEMATECH e-Handbook of Statistical Methods, 6.1.6 What is Process Capability?, National Institute of Standards and Technology, 2012
- NIST/SEMATECH e-Handbook of Statistical Methods, 6.3.2 What are Variables Control Charts?, National Institute of Standards and Technology, 2012
- Production Part Approval Process (PPAP), 4th edition, Automotive Industry Action Group, 2006
- Measurement Systems Analysis (MSA), 4th edition, Automotive Industry Action Group, 2010