Cpk vs Ppk: Which Capability Index Your Buyer Means (Worked Example)

Cpk and Ppk use the same formula. What differs is the standard deviation inside it. Cpk uses the spread within small subgroups of readings taken close together; Ppk uses the standard deviation of every reading in the study. If your spreadsheet runs STDEV over all the readings, the number it prints is Ppk, whatever the column is called. On a process that shifts between lots, the two can land either side of a buyer’s 1.33.

The worked example below shows how far apart they can be on one set of fabric-weight readings, and it is run in this site’s process capability calculator so you can repeat it with your own figures.

Cpk vs Ppk: the short answer

• Cp and Cpk use the within-subgroup standard deviation, usually estimated from the average subgroup range. They describe what the process holds while nothing changes.
• Pp and Ppk use the overall standard deviation of all the readings. They describe what was delivered over the study period, lot changes and drift included.
• A spreadsheet’s STDEV or STDEV.S over all readings gives Ppk, even in a cell labelled Cpk.
• If the buyer’s requirement does not say which index or which estimate of spread, ask. If the buyer will recalculate from your raw readings with a spreadsheet, expect them to get Ppk.
• When Cpk and Ppk disagree, the gap is the finding: something moved between subgroups.

The four indices and the question each one answers

All four compare the specification with the spread of the process. Cp and Pp ignore where the process sits. Cpk and Ppk measure to the nearer limit, so they fall when the mean moves off target even if the spread has not changed (NIST/SEMATECH e-Handbook, process capability).

The formulas: Cp = (USL − LSL) ÷ 6σ, and Cpk = the smaller of (USL − mean) and (mean − LSL), divided by 3σ. Pp and Ppk are the same, with the overall σ. The within-subgroup σ is estimated as the average subgroup range divided by a constant, R̄ ÷ d2, or as the average subgroup standard deviation divided by c4 (NIST/SEMATECH, X-bar and R charts). d2 is the expected range of n readings from a normal distribution with a standard deviation of 1; for subgroups of five it is 2.326 (Minitab’s table of d2).

Minitab’s documentation puts the difference in the customer’s terms. Within, or “potential”, capability is how the process could perform if the shifts and drifts between subgroups were removed; overall capability is what the customer experiences over time (Minitab, potential and overall capability). The international standard on the subject, ISO 22514-2, was revised in February 2026: the third edition replaces the 2017 one and deals with capability and performance for processes that do not stay in statistical control (ISO).

Worked example: finished GSM against 180 ± 8 g/m²

The readings are invented for this page; they are not a mill’s data. A knit fabric is finished on a stenter to a buyer’s specification of 180 ± 8 g/m², so the lower limit is 172 and the upper 188. Over two weeks the range finishes five greige lots. Quality takes five subgroups from each lot. Each subgroup is five discs cut across the width at one point in a roll and weighed one by one. That is 25 subgroups and 125 readings.

Within a lot the stenter holds weight well. Between lots it does not: the greige weight changes from lot to lot and the settings are not adjusted for it, so two lots finish heavy.

All 125 readings lie between 175.7 and 186.1 g/m², inside the specification. The grand mean is 181.00, the average subgroup range is 4.068, and the standard deviation of all 125 readings is 2.3329.

What goes into the calculator

Open the calculator with these figures already entered.

What the calculator shows

Same fabric, same 125 readings: one index meets the buyer’s 1.33, the other does not come close.

The same thing in a spreadsheet

Put the readings in a sheet with one subgroup per row, in cells B2 to F26. Then:

• =MIN(188-AVERAGE(B2:F26),AVERAGE(B2:F26)-172)/(3*STDEV.S(B2:F26)) returns 1.00. That is Ppk. Excel’s STDEV.S, and the older STDEV, estimate a standard deviation from a sample, dividing by n − 1, over every value they are given (Microsoft, STDEV.S function). They know nothing about subgroups, so the lot-to-lot shift goes straight into the result.
• For Cpk, add a column with each row’s range, =MAX(B2:F2)-MIN(B2:F2), average it (4.068), divide by 2.326 (1.749), and use that in place of STDEV.S. The result is 1.33.

So a report template whose “Cpk” cell is built on STDEV over all readings has been reporting Ppk all along. That is not a dishonest number; it is arguably the more useful one. But it is not what the label says, and the buyer may be setting it beside another supplier’s true Cpk.

The opposite mistake hides the gap. If each “subgroup” is five readings spread across a shift, or one disc from each of five rolls, the drift is already inside every range, the within-subgroup sigma swells, and Cpk falls to Ppk for the wrong reason. A subgroup should be readings taken so close together that only ordinary variation can act between them.

The 125 readings

Copy the table into a spreadsheet to reproduce every figure above. Readings in g/m².

Why the same fabric shows Cpk 1.33 and Ppk 1.00

The mean and the limits are the same for both indices, so the ratio between them is simply the ratio of the two standard deviations: 1.749 g/m² within subgroups against 2.333 overall. The overall variance is roughly the within-subgroup variance plus the variance between subgroups, so the lots differ with a standard deviation of about √(2.333² − 1.749²) = 1.54 g/m². The lot table shows it: lots 2 and 4 finished about 1.6 g/m² above the grand mean, lots 1 and 3 about as far below.

Inside any one lot, the stenter is as capable as Cpk says. On the within-subgroup spread, the normal model puts about 31 ppm above the upper limit. On the overall spread, the calculator expects 1,405.32 ppm, both limits together. The buyer receives the second figure.

Nor do 125 good readings disprove it. At that rate a 125-reading study would be expected to catch 0.18 out-of-specification readings, so finding none is the most likely outcome.

• Remove the lot shift and Ppk rises to meet Cpk. In the calculator, set the overall standard deviation to 1.749 (the within-subgroup sigma) and Ppk becomes 1.33, with 31.51 ppm expected. The stenter does not need to get better; the lots need to finish to the same mean, which means adjusting the finishing settings to each lot’s greige weight.
• Cpk 1.33 is an estimate. From 125 readings the calculator’s 95 percent lower confidence bound on Cpk is 1.19. A buyer who reads “Cpk ≥ 1.33” as a demonstrated minimum rather than a point estimate would not accept this study either.

Which index does your buyer mean?

Start with the buyer’s own document. A requirement that names the index, the estimate of spread, the subgroup size and the number of readings needs no interpretation. The trouble starts with a line that says only “Cpk ≥ 1.33”.

Automotive approval. Supply chains that use the AIAG Production Part Approval Process (PPAP) separate the two explicitly. As quoted from the 1995 AIAG manuals by Steiner, Abraham and MacKay of the University of Waterloo (Understanding Process Capability Indices), the PPAP manual told suppliers to calculate Ppk for the initial study. Above 1.67 the process probably met requirements; between 1.33 and 1.67 production could start, with extra attention until an ongoing Cpk of at least 1.33 was shown; below 1.33 the supplier needed a corrective action plan and, normally, increased inspection. The QS-9000 requirements of the same year set defaults of Cpk ≥ 1.33 for stable processes and Ppk ≥ 1.67 for chronically unstable but predictable ones. The long-standing convention is therefore Ppk ≥ 1.67 at approval and Cpk ≥ 1.33 in production. AIAG has revised these manuals since and sells them; we have not read the current editions, so confirm the figures in your customer’s own requirements.

Other buyers mix the two. Enerpac’s supplier PPAP manual (revision 2.0, January 2021), to take one published example, asks for Cpk for a new part or a changed process, and for Ppk when a supplier new to Enerpac already makes the part or has shipped a large number of nonconforming parts. It sets 1.33 as the minimum, 1.67 for safety characteristics, and at least 25 subgroups containing 100 readings (Enerpac Supplier PPAP Manual). Minitab notes that many industries use 1.33 as the benchmark (Minitab, key results).

Where the requirement is silent:

• If you send raw readings, a buyer who runs STDEV over them gets Ppk, and one who uses Minitab gets both, with a Cpk from a different within-subgroup estimate (next section). Report both yourself so the comparison is like for like.
• A study drawn from one lot, one shift or one machine setting cannot show between-lot variation, so even its Ppk is a short-term figure. Say what period, and how many lots, the study covers.
• Ask whether 1.33 is a point estimate or a lower confidence bound, and over how many readings.

The Waterloo authors go further and argue that Ppk is the index to report, because the customer cares about all the variation, whatever its source. Reporting both, with the gap, gives the buyer that and gives you the diagnosis.

Why two programs print different Cpk for the same readings

The within-subgroup sigma can be estimated in three common ways, and they do not agree to the second decimal:

On these readings the three within-subgroup estimates give Cpk from 1.32 to 1.35, which straddles 1.33. None comes near the overall figure. Arguing over the second decimal of Cpk while Ppk is 1.00 is arguing over the wrong number.

What the index numbers mean in parts per million

For a normal distribution, an index of 1.00 puts the nearer limit three standard deviations from the mean, 1.33 puts it four, and so on. The expected fraction beyond the limit follows from that.

The figures are the standard normal tail at three times the index. The NIST/SEMATECH e-Handbook gives 0.27 percent, 64 ppm, 0.6 ppm and 2 ppb for centred processes at Cp 1.00, 1.33, 1.66 and 2.00 (NIST); the small differences come from whether 1.33 is read as exactly 4/3. For an off-centre process only the first column matters, because the far tail is negligible. All of it assumes the readings are normal and the process stable. Attached to Cpk, these rates describe the short term; attached to Ppk, the delivered output.

And “3.4 defects per million”? That Six Sigma figure is not what an index of 2.00 means. It rests on a convention that the mean will wander by 1.5 standard deviations over the long term; Minitab describes the 1.5σ shift as what practitioners usually assume, and notes that the method differs between industries and companies (Minitab, Z.bench and sigma capability). A process with Cp 2.00 moved 1.5σ off centre has Cpk 1.50, and the normal tail beyond 4.5σ is 3.4 ppm. Without the shift, a centred Cp 2.00 process gives 0.002 ppm. Comparing Cpk with Ppk measures the long-term shift on your own process instead of assuming it.

What to send with a capability figure

• Both indices, Cpk and Ppk, with the specification limits and the grand mean; Cp and Pp too if the buyer asks.
• How the within-subgroup sigma was estimated (range, standard deviation or pooled), the subgroup size, how a subgroup was formed, and the number of subgroups and readings.
• The period and the lots the study covers.
• An X-bar and R chart, so the buyer can see whether the gap comes from a few lots or from steady drift (the control chart selector helps choose the chart), and a histogram.
• The lower confidence bound on Cpk, so the uncertainty is on the page.
• For weight measured on small discs, the measuring system’s share of the spread: a gauge R&R study shows how much of the within-subgroup range is the balance and the cutter rather than the fabric.

How this page is kept

Last verified: 3 October 2026. The worked example uses readings invented for this page. Every figure attributed to the calculator was computed with the calculator’s own formula and checked on the calculator page through the link above. Definitions and constants come from the NIST/SEMATECH e-Handbook and Minitab’s documentation, spreadsheet behaviour from Microsoft’s function reference, and buyer requirements from the documents named, each linked where it is used. The page describes published practice and requirements; your buyer’s own specification governs your product. Corrections are welcome through the contact page.