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Engineering calculator

Process Capability Cpmk Calculator

Compute Taguchi Cpmk from μ, σ, LSL, USL, and a target. Runs locally. Not Cpm, not Cpk, not Ppm, and not a 1.33 verdict.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Source checked · 7/7 tests · Production surface contract 4/4 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
Model
Taguchi Cpmk from stated μ, σ, LSL, USL, and a target.
Scope
Taguchi Cpmk = min(USL−μ, μ−LSL)/(3√(σ²+(μ−target)²)) from stated μ, σ, LSL, USL, and target.
Verification
Engine tested · 7/7 tests · Production surface contract 4/4 · Source checked · v1.0.0
Named expert review
Optional · Not performed
Sources
  • Pearn, Kotz, and Johnson — Distributional and inferential properties of process capability indices — Cpmk combines Cpk’s nearer side with Cpm’s Taguchi denominator
  • ISO 22514-2 — Statistical methods in process management — Capability and performance — Capability vs performance; target-based indices
Sources
Evidence
4 boundary · 3 property · Production surface contract 4/4 · Artifact integrity PASS
Production
Embedded snapshot: STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-16T06:44:24.909Z
Semantic contract
PASS

Formulas

Core equations used by this calculator.

CpmkCpmk = min(USL − μ, μ − LSL) / (3 √(σ² + (μ − target)²))
itarget is a process target, not tolerance span T. This is not Cpm (two-sided span in the numerator), not Cpk (no target in the denominator), and not Ppm (sample s).

How to use

1

Enter specification limits

LSL and USL in the same unit as μ, σ, and the target. USL must be greater than LSL.

2

Enter μ, σ, and the target

σ must be greater than zero. The target may sit anywhere; it is not required to be the spec midpoint.

3

Read Cpmk

On target at the midpoint, Cpmk equals Cpm. Off center, Cpmk is the nearer-side Taguchi index. Use Cpk when you have no target.

Example calculations

Common configurations with formula and result.

ϟ

On target

LSL=0 · USL=12 · μ=6 · σ=1 · target=6

Cpmk=6/(3·1)
Cpmk=2
ϟ

Off target

LSL=0 · USL=12 · μ=7 · σ=1 · target=6

Cpmk=5/(3√2)
Cpmk=5/(3√2)

Process Capability Cpmk calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Cpmk = min(USL − μ, μ − LSL) / (3 √(σ² + (μ − target)²)). Design-stage from a stated mean, σ, two-sided spec, and a target. When μ equals the target at the spec midpoint, Cpmk equals Cpm.
What it calculates
Taguchi Cpmk from stated μ, σ, LSL, USL, and a target.
Inputs
  • lsl
  • usl
  • mu
  • sigma
  • target
Outputs
  • Cpmk
  • offset
  • target
Formula
Cpmk=min(USL−μ,μ−LSL)/(3√(σ²+(μ−target)²))
Assumptions
  • Taguchi Cpmk = min(USL−μ, μ−LSL)/(3√(σ²+(μ−target)²)) from stated μ, σ, LSL, USL, and target.
  • Not Cpm (two-sided span), not Cpk (no target in the denominator), not Ppm, and not a 1.33 verdict.
Units
  • dimensionless
Boundary conditions
  • missing target → MISSING_REQUIRED_INPUT
  • sigma ≤ 0 → VALUE_MUST_BE_POSITIVE
  • USL ≤ LSL → INVALID_INPUT
Example
lsl=0 usl=12 mu=6 sigma=1 target=6 → Cpmk=2
Validation cases

3 published on this page · 7/7 tests · Production surface contract 4/4 · View evidence

  • lsl=0 usl=12 mu=6 sigma=1 target=6 → Cpmk=2
  • lsl=0 usl=12 mu=7 sigma=1 target=6 → Cpmk=5/(3√2)
  • missing target → MISSING_REQUIRED_INPUT
Sources
  • Pearn, Kotz, and Johnson — Distributional and inferential properties of process capability indices — Cpmk combines Cpk’s nearer side with Cpm’s Taguchi denominator
    Supports: Cpmk is not Cpm and not Cpk
  • ISO 22514-2 — Statistical methods in process management — Capability and performance — Capability vs performance; target-based indices
    Supports: This page is a design-stage target index, not overall sample Ppm
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute Taguchi Cpmk.

Supported and not supported

Supported — Cpmk from stated μ, σ, LSL, USL, and a target · API engineering.process.cpmk

Not supported — Cpm, Cpk, Ppm, Cpmk≥1.33 verdict, P/T = 1/Cp

Calculator URL stays /calc/engineering/process-capability-cpmk. There is no /calc/metrology.

Other calculators in this family: Process capability (Cpm), Process capability (Cp/Cpk), Process performance (Ppm), Process performance (Pp/Ppk), Process performance (Ppmk), Guard band, Tolerance / Uncertainty Workspace .

Cpm Process capability (Cpm) › Cp Process capability (Cp/Cpk) › Ppm Process performance (Ppm) › Pp Process performance (Pp/Ppk) › Ppmk Process performance (Ppmk) › GB Guard band › WS Tolerance / Uncertainty Workspace ›
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Frequently asked questions

Key distinctions behind the calculation.

Is Cpmk the same as Cpm?

No. Cpm uses the two-sided span (USL − LSL) in the numerator. Cpmk uses the nearer side, like Cpk. When the mean equals the target at the midpoint, they match.

Is this Cpk?

No. Cpk has no target in the denominator. Cpmk puts √(σ² + (μ − target)²) there.

Is this Ppm?

No. Ppm uses overall sample s from observations. Cpmk is design-stage from a stated μ and σ.

Does Cpmk≥1.33 mean pass?

This page does not issue that verdict. It reports Cpmk only.

Is target the same as tolerance T?

No. target is the process aim. TUR and Cg use T as a specification span. Do not send T as the target.

Where does this run?

Locally in the browser by default. REST and MCP call the same metrology-engine cpmk op.