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Engineering calculator

Process Performance Ppmk Calculator

Compute overall Taguchi Ppmk from observations, LSL, USL, and a target. Runs locally. Not Cpmk, not Ppk, not Ppm, and not a 1.33 verdict.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Overall Taguchi Ppmk from a sample, LSL, USL, and a target, + O3 mpmath tabulated Ppmk.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
Overall Taguchi Ppmk from a sample, LSL, USL, and a target, + O3 mpmath tabulated Ppmk.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (on-target, off-target, alias, awkward, invalid-domain) · Matrix
Deferred
Not design-stage Cpmk, not Ppk, and not a Ppmk≥1.33 verdict.
Numerical scope
O2: overall Taguchi Ppmk vs a separate-module sample identity (≤2 ULP). Not design-stage Cpmk, not Ppk, and not a Ppmk≥1.33 verdict. ≤2 ULP vs O3 applies only to the published tabulated Ppmk vectors (on target, off target, below target, an alias, a wider sample, a target away from the midpoint, one awkward sample, and ddof=0). It is not a whole-domain guarantee and does not cover design-stage Cpmk, Ppk, or a Ppmk≥1.33 verdict.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Overall Taguchi Ppmk from process observations, LSL, USL, and a target.
Scope
Overall Taguchi Ppmk = min(USL−x̄, x̄−LSL)/(3√(s²+(x̄−target)²)) from a sample. s is summarizeSample.
Verification
Engine tested · Source checked · v1.0.1 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Overall Taguchi Ppmk from a sample, LSL, USL, and a target, + O3 mpmath tabulated Ppmk.· 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 49bb2b418d18
Legacy regression
10/10 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 · 6/6 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 one-sided Taguchi; overall analog uses sample s
  • ISO 22514-2 — Statistical methods in process management — Capability and performance — Capability vs performance; target-based indices
Sources
Evidence
1 legacy golden · 6 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 6/6 invalid · Artifact integrity PASS
This calculator CURRENT · Public schema 1.0.1 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

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

Formulas

Core equations used by this calculator.

PpmkPpmk = min(USL − x̄, x̄ − LSL) / (3 √(s² + (x̄ − target)²))
is is the overall sample standard deviation of the entered values. target is a process target, not tolerance span T. This is not design-stage Cpmk, not Ppk (no target), and not Ppm (two-sided span).

How to use

1

Enter process observations

Comma, space, or semicolon separated. JSON arrays also work. Sample s needs at least two values when ddof=1.

2

Enter specification limits and the target

LSL and USL in the same unit as the observations. USL must be greater than LSL. The target may sit anywhere; it is not required to be the spec midpoint.

3

Read Ppmk

On target at the midpoint, Ppmk equals Ppm. Off center, Ppmk is the nearer-side Taguchi index from sample s. Use Cpmk when you already have a stated μ and σ.

Example calculations

Common configurations with formula and result.

ϟ

On target

values=4, 6, 8 · LSL=0 · USL=12 · target=6

s=2; Ppmk=6/(3·2)
Ppmk=1
ϟ

Off target

values=7, 8, 9 · LSL=0 · USL=12 · target=6

s=1; Ppmk=4/(3√5)
Ppmk=4/(3√5)

Process Performance Ppmk calculator specification

Version 1.0.1 · Engine tested

Calculation status

Review policy · Evidence

Definition
From n observations, x̄ and s are the overall sample mean and standard deviation (ddof=1). Ppmk = min(USL − x̄, x̄ − LSL) / (3 √(s² + (x̄ − target)²)).
What it calculates
Overall Taguchi Ppmk from process observations, LSL, USL, and a target.
Inputs
  • values
  • lsl
  • usl
  • target
  • ddof
Outputs
  • Ppmk
  • offset
  • target
  • xbar
  • s
  • n
Formula
Ppmk=min(USL−x̄,x̄−LSL)/(3√(s²+(x̄−target)²))
Assumptions
  • Overall Taguchi Ppmk = min(USL−x̄, x̄−LSL)/(3√(s²+(x̄−target)²)) from a sample. s is summarizeSample.
  • Not design-stage Cpmk, not Ppk (no target), not Ppm (two-sided span), and not a 1.33 verdict.
Units
  • dimensionless
Boundary conditions
  • missing target → MISSING_REQUIRED_INPUT
  • n=1 with ddof=1 → VALUE_OUT_OF_RANGE
  • s=0 and x̄=target → VALUE_MUST_BE_POSITIVE
  • USL ≤ LSL → INVALID_INPUT
Example
values=4,6,8 lsl=0 usl=12 target=6 → Ppmk=1
Validation cases

3 published on this page · 10/10 tests · Production surface contract 6/6 · View evidence

  • values=4,6,8 lsl=0 usl=12 target=6 → Ppmk=1
  • values=7,8,9 lsl=0 usl=12 target=6 → Ppmk=4/(3√5)
  • missing target → MISSING_REQUIRED_INPUT
Sources
  • Pearn, Kotz, and Johnson — Distributional and inferential properties of process capability indices — Cpmk one-sided Taguchi; overall analog uses sample s
    Supports: Ppmk is the overall-sample counterpart of Cpmk
  • ISO 22514-2 — Statistical methods in process management — Capability and performance — Capability vs performance; target-based indices
    Supports: This page is overall performance, not design-stage Cpmk
Calculation version
1.0.1

Background

Interpretation and common distinctions.

Compute overall Taguchi Ppmk.

Supported and not supported

Supported — Ppmk from observations, LSL, USL, and a target · API engineering.process.cpmk_performance

Not supported — design-stage Cpmk, Ppk, Ppm, Cpmk≥1.33 / Ppmk≥1.33 verdict, P/T = 1/Cp

Calculator URL stays /calc/engineering/process-performance-ppmk. There is no /calc/metrology.

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

Cpmk Process capability (Cpmk) › Ppm Process performance (Ppm) › Pp Process performance (Pp/Ppk) › Cpm Process capability (Cpm) › GB Guard band › WS Tolerance / Uncertainty Workspace ›

Frequently asked questions

Key distinctions behind the calculation.

Is this the same as Cpmk?

No. Cpmk is design-stage from a stated μ and σ. This page takes observations and uses overall s. The formulas look alike; the σ is not the same contract.

Is this Ppk?

No. Ppk has no target in the denominator. Ppmk puts √(s² + (x̄ − target)²) there.

Is this Ppm?

No. Ppm uses the two-sided span (USL − LSL) in the numerator. Ppmk uses the nearer side, like Ppk.

Does Ppmk≥1.33 mean pass?

This page does not issue that verdict. It reports Ppmk 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_performance op.