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Engineering calculator

Process Performance Ppm Calculator

Compute overall Taguchi Ppm from observations, LSL, USL, and a target. Runs locally. Not design-stage Cpm, not Pp/Ppk, and not a 1.33 verdict.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Source checked · 9/9 tests · Production surface contract 4/4 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
Model
Overall Taguchi Ppm from process observations, LSL, USL, and a target.
Scope
Overall Taguchi Ppm = (USL−LSL)/(6√(s²+(x̄−target)²)) from a sample. s is summarizeSample.
Verification
Engine tested · 9/9 tests · Production surface contract 4/4 · Source checked · v1.0.0
Named expert review
Optional · Not performed
Sources
  • Chan, Cheng, and Spiring — A new measure of process capability: Cpm — Cpm = (USL−LSL)/(6√(σ²+(μ−T)²)); overall analog uses sample s
  • ISO 22514-2 — Statistical methods in process management — Capability and performance — Capability vs performance; target-based indices
Sources
Evidence
6 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.

PpmPpm = (USL − LSL) / (6 √(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 Cpm (stated μ, σ) and not Pp/Ppk (those have no target).

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 Ppm

On target, Ppm equals Pp. Off target, Ppm is smaller. Use Cpm 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; Ppm=12/(6·2)
Ppm=1
ϟ

Off target

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

s=1; Ppm=12/(6√5)
Ppm=2/√5

Process Performance Ppm calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
From n observations, x̄ and s are the overall sample mean and standard deviation (ddof=1). Ppm = (USL − LSL) / (6 √(s² + (x̄ − target)²)).
What it calculates
Overall Taguchi Ppm from process observations, LSL, USL, and a target.
Inputs
  • values
  • lsl
  • usl
  • target
  • ddof
Outputs
  • Ppm
  • offset
  • target
  • xbar
  • s
  • n
Formula
Ppm=(USL−LSL)/(6√(s²+(x̄−target)²))
Assumptions
  • Overall Taguchi Ppm = (USL−LSL)/(6√(s²+(x̄−target)²)) from a sample. s is summarizeSample.
  • Not design-stage Cpm, not Pp/Ppk (no target), 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 → Ppm=1
Validation cases

3 published on this page · 9/9 tests · Production surface contract 4/4 · View evidence

  • values=4,6,8 lsl=0 usl=12 target=6 → Ppm=1
  • values=7,8,9 lsl=0 usl=12 target=6 → Ppm=2/√5
  • missing target → MISSING_REQUIRED_INPUT
Sources
  • Chan, Cheng, and Spiring — A new measure of process capability: Cpm — Cpm = (USL−LSL)/(6√(σ²+(μ−T)²)); overall analog uses sample s
    Supports: Ppm is the overall-sample counterpart of Cpm
  • 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 Cpm
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute overall Taguchi Ppm.

Supported and not supported

Supported — Ppm from observations, LSL, USL, and a target · API engineering.process.cpm_performance

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

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

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

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

Key distinctions behind the calculation.

Is this the same as Cpm?

No. Cpm 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 Pp/Ppk?

No. Pp/Ppk have no target in the denominator. When the mean equals the target, Ppm equals Pp. This page does not report Ppk.

Does Ppm≥1.33 mean pass?

This page does not issue that verdict. It reports Ppm 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 cpm_performance op.