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Cm / Cmk (Pm / Pmk) machine capability calculator

Paste the parts from a machine buy-off with your tolerance and get Cm and Cmk — the AIAG-VDA manual's Pm and Pmk — with the spread convention stated and the run order charted.

How you calculate Cmk in Excel

Put the parts in a column, take AVERAGE and STDEV.S, then (USL − mean) / (3 × s) and (mean − LSL) / (3 × s), and MIN of the two. For the 8s convention it is 4 × s instead of 3 × s. Here STDEV.S is the right sigma — a machine study has no subgroups to take a within estimate from.

The formula is the easy part. What the spreadsheet will not tell you is whether the machine held still while those parts were made: a run that drifted from warm-up to steady state gives a perfectly respectable Cmk for a machine that does not exist.

Nothing you paste leaves this calculation. It is not stored, not logged and not sent anywhere else — the numbers are computed and returned, and that is all. Paste straight out of a spreadsheet — tab-separated columns are understood as they land.

One reading per line, ideally 50 consecutive parts. Commas, tabs and semicolons all work; a header row is ignored.

How this is calculated

A machine study takes consecutive parts off one machine — one setting, one operator, one batch of material — so that only the machine and the gauge contribute variation. Its sigma is the plain sample standard deviation s of those parts: a short run has no subgroups to take a within estimate from. 

Pm  = Cm  = (USL − LSL) / (k · s)
Pmk = Cmk = min(USL − x̄, x̄ − LSL) / ((k / 2) · s)

k = 6 (as Cp/Cpk) or 8 (stricter procedures)

With one specification limit there is no Pm, and Pmk is the side you gave.

Cm or Pm?

The same numbers. The AIAG & VDA SPC manual of July 2026 keeps the letter C for a process shown to be stable, as the ISO 22514 series does. A machine study is too short to show that, so the manual reports it as machine performance, Pm/Pmk. Suppliers working to VDA have called it Cm/Cmk for decades; a customer on the new manual will ask for Pm/Pmk. More on the manual on what the AIAG & VDA manual changed.

6s or 8s

Procedures disagree, and the page asks rather than guessing. Over 8s the same machine scores three quarters of its 6s figure, so a Cmk of 1.67 over 8s is a Cmk of 2.22 over 6s. Quote the spread with the number, or the number cannot be compared with anything.

Why the chart

The index assumes the machine held still while the parts were made. Warm-up, tool wear or a change of material during the run all widen s and say nothing about why. The individuals chart of the run in order shows it; a signal there means the study describes that run, not the machine. Once the machine is in production, the Cp/Cpk calculator takes over, and the confidence calculator says how much fifty parts can prove.

What the Excel version will not do

Nothing checks the run order
A machine study assumes the parts came off a stable machine. A trend through the sample — tool wear, warm-up — inflates s and says nothing about why. Charting the run in order is the check, and a column of numbers does not do it.
The convention is invisible
A cell holding 1.71 does not say whether it was divided by 6s or 8s, or which name the customer expects. Two engineers comparing numbers can be a factor of 0.75 apart and both right.

Questions people ask about this

What is the difference between Cm/Cmk and Cp/Cpk?

The data, not the formula. Cm and Cmk come from a short run of consecutive parts off one machine, at one setting, with one operator and one batch of material, so only the machine and the gauge contribute variation. Cp and Cpk come from the running process over time, with every other source of variation included. That is why the machine requirement is usually set higher: the process will only add to what the machine shows.

Why does the AIAG-VDA manual call them Pm and Pmk?

Because the AIAG & VDA SPC manual of July 2026 keeps the letter C for a process shown to be stable, in line with the ISO 22514 series. A machine study is too short to show stability, so it reports "machine performance": Pm and Pmk. The arithmetic is what VDA suppliers have always called Cm and Cmk; only the name says less than it used to.

Should Cm be calculated over 6s or 8s?

It depends on whose procedure you are working to, which is why this page asks. Minitab computes Cm and Cmk with the Cp and Cpk formulas, over 6s. Some procedures divide the tolerance by 8s instead, which is stricter: the same machine scores three quarters of the 6s figure. A Cmk quoted without its spread cannot be compared with anything.

What is a good Cmk?

1.67 is the benchmark most often quoted, and it is the default here. Your customer's manual decides; some set a higher value for Cm than for Cmk. Whatever the number, check it against the spread it was written for.

How many parts does a machine capability study need?

Fifty consecutive parts is the usual figure, and 20 to 50 is the range Minitab gives. The parts must be consecutive and measured in the order they were made, so that drift during the run shows up — which is what the chart under the result is for.

The machine passed. Now watch the process.

A buy-off is one run on one day. A workspace charts the same characteristic as production runs, with limits locked at a baseline you choose and Cpk beside Ppk, so you see when the process starts adding to what the machine showed.

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More capability tools

  • Cp / Cpk calculator — Paste measurements — or type a mean and a sigma — with your tolerance, and get Cp, Cpk, Pp, Ppk, the sigma level and the expected parts per million out of spec.
  • Cpk confidence interval & sample size — A Cpk of 1.33 from 30 pieces has a 95% interval of roughly 0.97 to 1.69. See the uncertainty in your own number, and how many parts would settle it.
  • Cpk ↔ PPM ↔ sigma level converter — What PPM is a Cpk of 1.33? What Cpk does 3.4 PPM need? Both conventions shown side by side, because the 1.5 sigma shift is why two sources disagree by a factor of ten.

Everything else

  • Control limit calculator — Give it subgroups or individual readings and it returns the control limits for the chart, the range or sigma chart beneath it, and every constant it used to get there.
  • Control chart generator — Paste a column of numbers, or rows of subgroups, and get a real control chart: limits from the data, Nelson rules 1–4 evaluated, out-of-control points marked.
  • Nelson & Western Electric rules checker — Every run rule evaluated on your data, each violation named in plain English with what it usually indicates — a shift, a trend, tool wear, two machines mixed.
  • Control chart constants — The whole table, n = 2 to 25, with the formula each constant belongs to. The same values the charts on this site are computed from.
  • X̄-R chart calculator — Subgroups in, X̄ and R charts out — limits from A₂, D₃ and D₄, run rules evaluated, and the range chart shown first because it decides whether the averages chart can be trusted.
  • X̄-s chart calculator — For subgroups big enough that the range wastes them. Limits from A₃, B₃ and B₄, sigma recovered with the c₄ correction, and the s chart read first because it decides whether the averages chart can be trusted.
  • I-MR chart calculator — For processes that give you one number at a time — a batch, an oven, a destructive test. Limits from the mean moving range, run rules evaluated, and an honest note about what an individuals chart cannot see.
  • Levey-Jennings chart with Westgard rules — Paste your QC results with the assigned mean and SD from the package insert, and get the chart with every sigma band drawn and all six Westgard rules evaluated — each one named, and labelled random or systematic error.
  • Bland-Altman plot — Paired readings from two methods, plotted as difference against average — with the bias, the limits of agreement, their confidence intervals, and a test for whether the disagreement depends on the magnitude.
  • Pareto chart generator — Categories and counts in, ranked bars and the cumulative line out — with the vital few named, an "Other" bucket that always sorts last, and an honest warning when the distribution is flat and there is no dominant cause to attack.
  • Box and whisker plot generator — One column per group, boxes side by side. Quartiles, the 1.5×IQR fences, whiskers that stop at real readings and outliers drawn individually — with the quartile method stated, because that is why your plot and Excel's disagree.
  • Histogram and normality test — A histogram with the fitted normal curve, both standard bin rules with a reasoned recommendation, and an Anderson-Darling test that refuses to tell you your data is normal — because no test can.
  • Gage R&R calculator (ANOVA) — Paste a crossed study — part, operator, reading — and get the full ANOVA: repeatability and reproducibility separated, the part-by-operator interaction tested rather than assumed away, %GRR, %Tolerance and ndc against AIAG's bands.
  • p, np, u and c chart calculator — Counted data rather than measured: proportion defective, number defective, defects per unit. Limits that step with the sample size instead of pretending it never changed, and an honest warning when the counts are too low for three-sigma limits to mean anything.
  • Grubbs outlier test — The G statistic against its critical value, the p-value, and the point implicated — plus a straight answer about what to do next, which is almost never to delete the reading.
  • Scatter diagram and correlation — Paired readings plotted, with Pearson r, Spearman rho, r², the least-squares line and its p-value — and the two reported together, because when they disagree the disagreement is the finding.
  • Standard deviation calculator — The usual summary statistics, and the thing a spreadsheet will not tell you: the within-subgroup sigma a control chart uses, beside the overall sigma a textbook means. The gap between them is why Cpk and Ppk disagree.
  • SEMI E10 / E79 equipment metrics calculator — One line per month with the hours in each state and the failure count. You get every E10 metric per period and for the whole window, OEE if you give the rated throughput, and the metric you choose drawn on an individuals chart with limits — so the question "did reliability actually change?" gets an answer instead of an argument.