Engineering calculator

Process Performance Calculator (Pp / Ppk)

Q: 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.

Q: 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.

Q: Where does this run?

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

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 CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Overall Pp, Ppk, Ppu, Ppl from a sample standard deviation, + O3 mpmath tabulated Pp/Ppk.

Input interpretation: Enter values to calculate.
Result: —
Verified scope: Overall Pp, Ppk, Ppu, Ppl from a sample standard deviation, + O3 mpmath tabulated Pp/Ppk.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (centered, shifted, population, alias, invalid-domain) · Matrix
Deferred: Not design-stage Cp/Cpk from a stated σ, not Type A u_A = s/√n, and not Cpm.
Numerical scope: O2: overall Pp/Ppk from a sample vs a separate-module identity (≤2 ULP). Not design-stage Cp/Cpk, not Type A u_A = s/√n, and not Cpm. ≤2 ULP vs O3 applies only to the published tabulated process-performance vectors (centered, shifted, low, an alias, population ddof, a negative Ppk, four points, and one awkward sample). It is not a whole-domain guarantee and does not cover design-stage Cp/Cpk, Type A u_A, or Cpm.
Known limitations: Core CVP does not include live graph, viewport, or pointer interaction.
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 · Source checked · v1.0.1 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Overall Pp, Ppk, Ppu, Ppl from a sample standard deviation, + O3 mpmath tabulated Pp/Ppk.· View Manifest · CVP overview · Specification
Versions: Calculation 1.0.1 · CVP protocol 1.0.0-proposed · Evidence 2026-09-23.o2-o3
Verification revision: 2026-09-23.o2-o3 · 1/1 property · digest 46214495714e
Legacy regression: 8/8 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 · 5/5 CVP boundary · 8/8 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 3/3 cross-interface · 6/6 CVP contract · Manifest
Sources: NIST Engineering Statistics Handbook — Process Capability — 6.1.6 What is Process Capability?
AIAG SPC — Statistical Process Control — Process performance indices Pp, Ppk
Sources
Evidence: 1 legacy golden · 5 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 8/8 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.

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

Enter process observations

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

Enter specification limits

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

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.

Centered

values=4, 6, 8 · LSL=0 · USL=12

s=2; Pp=12/(6·2)

Pp=1 · Ppk=1

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 1.0.1 · Engine tested

Calculation status

Engine tested 8/8 tests · Production surface contract 6/6
Named expert review Not performed
Calculation version 1.0.1

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 · 8/8 tests · Production surface contract 6/6 · 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: 1.0.1

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 1.0.1.

{ "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.

Frequently asked questions

Key distinctions behind the calculation.

Is this the same as the Cp/Cpk page?