Cmk calculation: the machine capability index explained
You bought a new CNC, the supplier wants sign-off, and the contract says "demonstrate Cmk ≥ 1.67 over 50 parts." Cmk is the number that decides whether a machine is accepted at runoff. Here is how to calculate it, with a full worked example.
What Cmk actually measures
Cmk is the machine capability index. It answers a narrow question: can this one machine, on its own, hold the tolerance? To isolate the machine, a capability run is deliberately kept clean — around 50 consecutive parts, one operator, one batch of material, one setup, no tool changes, no interruptions. That way the spread you measure comes from the machine, not from shift changes or material lots.
This is why Cmk is the index used at machine runoff and acceptance (often part of a factory acceptance test), while Cpk is reserved for the running process. Both share the same maths; they differ in what variation they capture.
The Cmk formula
Two indices come out of a capability run. The potential index ignores where the process sits; the real index accounts for centring:
- Cm = (USL − LSL) / (6σ) — machine potential, assumes perfect centring
- Cmk = min[ (USL − x̄) / (3σ), (x̄ − LSL) / (3σ) ] — accounts for the offset from centre
Here x̄ is the mean of the run, σ is the standard deviation of all the measured parts, and USL and LSL are the upper and lower specification limits. Because Cmk takes the minimum of the two sides, an off-centre machine is penalised even if its spread is tiny.
Worked example
A new lathe is being accepted for turning a shaft diameter specified as ∅20.00 ±0.05 mm, so USL = 20.05 and LSL = 19.95. Fifty consecutive parts are turned and measured on a calibrated micrometer. The run gives:
- Mean, x̄ = 20.012 mm
- Standard deviation, σ = 0.008 mm
First the potential index:
| Step | Calculation | Result |
|---|---|---|
| Cm | (20.05 − 19.95) / (6 × 0.008) | 2.08 |
| Upper side | (20.05 − 20.012) / (3 × 0.008) | 1.58 |
| Lower side | (20.012 − 19.95) / (3 × 0.008) | 2.58 |
| Cmk | min(1.58, 2.58) | 1.58 |
The spread is excellent — Cm of 2.08 says the machine could comfortably hold the tolerance. But Cmk is only 1.58, below the usual 1.67 acceptance bar, because the mean sits 0.012 mm high. The fix is not a better machine, it is a tool offset. Shift the tool to centre the diameter at 20.00:
| Step | Calculation | Result |
|---|---|---|
| New mean | x̄ = 20.001 | — |
| Upper side | (20.05 − 20.001) / (3 × 0.008) | 2.04 |
| Lower side | (20.001 − 19.95) / (3 × 0.008) | 2.13 |
| Cmk | min(2.04, 2.13) | 2.04 |
Same machine, same spread, one offset correction, and Cmk jumps from 1.58 to 2.04. The runoff passes. You can check your own numbers with the Cp/Cpk calculator, which uses the identical centring maths.
Cmk vs Cpk vs Ppk
| Index | Captures | Sample | Used for |
|---|---|---|---|
| Cmk | One machine, short term | ~50 consecutive parts | Machine runoff / acceptance |
| Cpk | Process, within-subgroup sigma | 20–25 subgroups | Ongoing capability |
| Ppk | Process, overall sigma | Full production period | PPAP performance |
The logic flows in that order: prove the machine with Cmk, then prove the process with Cpk, then report long-term performance with Ppk to the customer. For the process-side detail see Cp vs Cpk explained and Cpk vs Ppk.
Acceptance limits
| Cmk | Verdict |
|---|---|
| ≥ 2.00 | Often required for new equipment |
| ≥ 1.67 | Standard machine acceptance bar |
| 1.33 – 1.67 | Conditional; adjust and re-run |
| < 1.33 | Reject the runoff |
Common mistakes
- Interrupting the run. A tool change or break midway adds variation that does not belong in a machine study.
- Mixing material lots. Two batches of bar stock inflate σ and hide the machine's true capability.
- Reporting Cm and calling it Cmk. Cm ignores centring; an off-centre machine can look fine on Cm and fail on Cmk.
- Too few parts. Thirty is a floor; fifty gives a far steadier estimate of σ.
- Non-normal data. Capability indices assume a roughly normal distribution. Check it before trusting the index.
Frequently asked questions
What is Cmk?
Cmk is the machine capability index. It measures how well one machine holds a dimension over a short, uninterrupted run of about 50 consecutive parts, so that only machine variation is captured.
What is a good Cmk value?
Most acceptance runs require Cmk ≥ 1.67, and many OEMs ask for 2.0 on new equipment. Below 1.33 the runoff normally fails.
How is Cmk different from Cpk?
Cmk is short term and isolates one machine for runoff. Cpk covers the running process over a longer period and includes shift, material and operator variation.
How many parts do I need?
Fifty consecutive parts is the common requirement; some standards accept a minimum of thirty.