HomeCalculatorsEngineeringProcess Performance Calculator (Pp / Ppk)
Engineering calculator

Process Performance Calculator (Pp / Ppk)

Compute overall Pp, Ppk, Ppu, and Ppl from process observations, LSL, and USL. σ is the overall sample s. Runs locally. Not design-stage Cp/Cpk and not Type A u_A.

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
Overall Pp, Ppk, Ppu, Ppl from process observations and two-sided limits.
Scope
Overall sample s via summarizeSample (ddof=1 default) — not a stated design σ
Verification
Engine tested · 7/7 tests · Production surface contract 4/4 · Source checked · v1.0.0
Named expert review
Optional · Not performed
Sources
Sources
Evidence
5 boundary · 2 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.

PpPp = (USL − LSL) / (6s)
PpuPpu = (USL − μ) / (3s)
PplPpl = (μ − LSL) / (3s)
PpkPpk = min(Ppu, Ppl)
is is the overall sample standard deviation of the entered values. This is not design-stage Cp/Cpk (stated μ, σ). It is not Type A u_A = s/√n.

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

LSL and USL in the same unit as the observations. USL must be greater than LSL.

3

Read Ppk, then Pp

Ppk is the primary index. Pp ignores centering. Use Process capability when you already have a stated μ and σ.

Example calculations

Common configurations with formula and result.

ϟ

Centered

values=4, 6, 8 · LSL=0 · USL=12

s=2; Pp=12/(6·2)
Pp=1 · Ppk=1
ϟ

Off-center

values=7, 8, 9 · LSL=0 · USL=12

s=1; Ppk=min((12−8)/3, (8−0)/3)
Pp=2 · Ppk=4/3

Process Performance Calculator (Pp / Ppk) specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
From n observations, μ = x̄ and s is the overall sample standard deviation (ddof=1). Pp = (USL − LSL) / (6s). Ppu = (USL − μ) / (3s). Ppl = (μ − LSL) / (3s). Ppk = min(Ppu, Ppl).
What it calculates
Overall Pp, Ppk, Ppu, Ppl from process observations and two-sided limits.
Inputs
  • values
  • lsl
  • usl
  • ddof
Outputs
  • Pp
  • Ppk
  • Ppu
  • Ppl
  • mu
  • sigma
  • n
Formula
Pp=(USL−LSL)/(6s); Ppk=min(Ppu,Ppl)
Assumptions
  • Overall sample s via summarizeSample (ddof=1 default) — not a stated design σ
  • Not design-stage Cp/Cpk and not Type A u_A
  • Not within-subgroup SPC and not Monte Carlo simulated indices
  • Two-sided limits; USL > LSL
Units
  • same as LSL/USL/values
Boundary conditions
  • missing values, lsl, or usl → MISSING_REQUIRED_INPUT
  • n < 2 when ddof=1 → VALUE_OUT_OF_RANGE
  • s = 0 → VALUE_MUST_BE_POSITIVE
  • USL ≤ LSL → INVALID_INPUT
Example
values=4,6,8 lsl=0 usl=12 → Pp=1 Ppk=1
Validation cases

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

  • values=4,6,8 lsl=0 usl=12 → Pp=1 Ppk=1
  • values=1 lsl=0 usl=12 → VALUE_OUT_OF_RANGE
Sources
  • NIST Engineering Statistics Handbook — Process Capability — 6.1.6 What is Process Capability?
    Supports: Pp/Ppk use overall (long-term) variation; Cp/Cpk use a stated or within σ
  • AIAG SPC — Statistical Process Control — Process performance indices Pp, Ppk
    Supports: Pp and Ppk use overall sample standard deviation
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute overall process performance from observations.

Supported and not supported

Supported — Two-sided Pp, Ppk, Ppu, Ppl from values · API engineering.process.performance

Not supported — Stated μ/σ (that is Cp/Cpk), Type A u_A, within-subgroup SPC, one-sided only, Monte Carlo simulated indices

Agent / API notes

Capability id: engineering.process.performance · tool id: process-performance · pin 1.0.0.

{ "values": [4, 6, 8], "lsl": 0, "usl": 12 }

Alias: sample for values. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, INVALID_INPUT, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE.

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

Other calculators in this family: Process capability (Cp/Cpk), Process capability (Cpm), Process performance (Ppm), Process performance (Ppmk), Type A uncertainty, Gauge R&R, Gauge capability (Cg/Cgk), Monte Carlo tolerance, Guard band, Tolerance / Uncertainty Workspace .

Cp Process capability (Cp/Cpk) › Cpm Process capability (Cpm) › Ppm Process performance (Ppm) › Ppmk Process performance (Ppmk) › uA Type A uncertainty › GRR Gauge R&R › Cg Gauge capability (Cg/Cgk) › MC Monte Carlo tolerance › GB Guard band › WS Tolerance / Uncertainty Workspace ›
}

Frequently asked questions

Key distinctions behind the calculation.

Is this the same as the Cp/Cpk page?

No. Process capability takes a stated μ and σ (design-stage). This page takes observations and computes overall s. The formulas look alike; the σ is not the same contract.

Is s the same as Type A u_A?

No. Type A reports u_A = s/√n of the mean. This page uses s itself in the 6s / 3s formulas.

Where does this run?

Locally in the browser by default. REST and MCP call the same metrology-engine process_performance ops.