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

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Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Design-stage Taguchi Cpmk from stated μ, σ, LSL, USL, and a target, + O3 mpmath tabulated Cpmk.

Input interpretation: Enter values to calculate.
Result: —
Verified scope: Design-stage Taguchi Cpmk from stated μ, σ, LSL, USL, and a target, + O3 mpmath tabulated Cpmk.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (on-target, off-target, alias, awkward, invalid-domain) · Matrix
Deferred: Not Cpm, not Cpk, not Ppmk from a sample, and not a Cpmk≥1.33 verdict.
Numerical scope: O2: design-stage Taguchi Cpmk vs a separate-module identity (≤2 ULP). Not Cpm, not Cpk, and not a Cpmk≥1.33 verdict. ≤2 ULP vs O3 applies only to the published tabulated Cpmk vectors (on target, off target, below target, an alias, a wider σ, a target away from the midpoint, one awkward sample, and a tiny offset). It is not a whole-domain guarantee and does not cover Cpm, Cpk, or a Cpmk≥1.33 verdict.
Known limitations: Core CVP does not include live graph, viewport, or pointer interaction.
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 · Source checked · v1.0.1 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Design-stage Taguchi Cpmk from stated μ, σ, LSL, USL, and a target, + O3 mpmath tabulated Cpmk.· View Manifest · CVP overview · Specification
Versions: Calculation 1.0.1 · CVP protocol 1.0.0-proposed · Evidence 2026-09-24.o2-o3
Verification revision: 2026-09-24.o2-o3 · 1/1 property · digest 1bc90998298e
Legacy regression: 7/7 tests · Production surface contract 6/6
Trust layers: Verification VERIFIED · Production CURRENT · Overall CVP state: VERIFIED under CVP 1.0.0-proposed
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Interfaces: PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
Supplemental domain review: Not performed
Named expert review: Not performed
CVP suite: 4/4 golden · 3/3 CVP boundary · 6/6 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 3/3 cross-interface · 6/6 CVP contract · Manifest
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: 1 legacy golden · 3 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 6/6 invalid · Artifact integrity PASS
Semantic contract: PASS

Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

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

Enter specification limits

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

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.

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.

On target

LSL=0 · USL=12 · μ=6 · σ=1 · target=6

Cpmk=6/(3·1)

Cpmk=2

Off target

LSL=0 · USL=12 · μ=7 · σ=1 · target=6

Cpmk=5/(3√2)

Process Capability Cpmk calculator specification

Version 1.0.1 · Engine tested

Calculation status

Engine tested 7/7 tests · Production surface contract 6/6
Named expert review Not performed
Calculation version 1.0.1

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 6/6 · 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: 1.0.1

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

Agent / API notes

Capability id: engineering.process.cpmk · tool id: cpmk · pin 1.0.1.

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 .

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.