Public evidence

engineering.tolerance.monte_carlo

Machine-checked verification for calculation version 1.12.0 · tier internally_reviewed

Open calculator API Capability Download JSON CVP Manifest Reproduce MCP Review policy

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · O2-A analytic σ/moments/Cp* and O2-B seeded mulberry32+Box-Muller replay of mean/std/percentiles/yield + O3 mpmath tabulated analytic σ. NORTA sampling and Sobol/Shapley remain Evidence regression.· 1-D MC stack; independent oracle covers analytic identities + seeded independent/joint-normal sampling; O3 covers tabulated analytic σ only · Protocol · Schema · Production report

Declared partition coverage: PASS · 13/13 declared partitions (normal-independent, normal-correlated, non-normal, norta-correlated, asymmetric, mean-shift, yield-capability, sensitivity-ranking, sobol, shapley, reproducibility, large-N, invalid-domain)
Versions: Calculation 1.12.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-16.o3-analytic
Verification revision: 2026-09-16.o3-analytic · 40/40 property · digest 964fa4df8516

Verification

Legacy regression suite: 71/71 calculation tests · Production surface contract 8/8

Three distinct suites: educational examples on the calculator page, this legacy regression count (71/71 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.12.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-09-16.o3-analytic. Calculation version 1.12.0. CVP 1.0.0-proposed. 5/5 golden · 25/25 CVP boundary · 13/13 invalid · 40/40 property · 8/8 O3 · 12/12 cross-interface · 8/8 CVP contract. digest 964fa4df8516. O2-A: analytic σ / moments / Cp* Cpk* vs separate-module identities (≤2 ULP). O2-B: seeded mulberry32+Box-Muller replay of mean/std/percentiles/yield (≤2 ULP). Not measured SPC. NORTA Pearson ≠ latent ρ; NORTA sampling remains Evidence regression. ≤2 ULP vs O3 applies only to the published tabulated analytic σ / moments / stack_center vectors (independent normal, correlated normal, gap, uniform, asymmetric uniform, triangular, k=1 3-4-5, single). Seeded MC statistics, NORTA, Sobol, and Shapley are not O3-compared.

Golden (oracle-backed) 5 / 5
CVP boundary 25 / 25
Invalid input 13 / 13
Property 40 / 40
O3 high-precision 8 / 8
Cross-interface 12 / 12
CVP contract 8 / 8
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session.
Verified scope O2-A analytic σ/moments/Cp* and O2-B seeded mulberry32+Box-Muller replay of mean/std/percentiles/yield + O3 mpmath tabulated analytic σ. NORTA sampling and Sobol/Shapley remain Evidence regression.
Assurance Engineering
Deferred NORTA sampling, Sobol, and Shapley remain Evidence regression. O3 does not cover seeded MC statistics, Gaussian copula, or GD&T/3-D chains.

contract page version PASS
contract capability version PASS
contract input schema version PASS
contract output schema version PASS
evidence version matches manifest PASS
schema valid input executes PASS
engine success output validates schema PASS
schema rejects incomplete input PASS

Fingerprint sha256:b4326f46a11710b3cbb4d2b124ac12ebc8e637d6d7e6dd9fbbbdcc2fd9c25a43

Input schema sha256:55ee91bbeba09c82e0effc6d2c3bf95a9e0d7afe24f8b056bf217788b81992b1 · Output schema sha256:6bd4d91cb24648c1c65224651fb3153e3b3c7149b5328f5362df59d0ec62744a · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Build & scope

Engine identity and declared limitations.

Tool: monte-carlo-tolerance
Engine: monte-carlo-tolerance
Engine build: 2026-09-11
Evidence core: 2026-09-11T23:04:52.544Z
Rendered: 2026-09-16T22:03:43.742Z
Last reviewed: 2026-08-12

Assumptions

Independent unless correlations provided
Correlated all-normal: joint two-piece normal via Cholesky
Correlated non-normal: Gaussian-copula NORTA; entered ρ is latent Gaussian correlation, not Pearson of the finished marginals
Cp*/Cpk* are design-stage simulated indices

Limitations

1-D stack; correlations use joint normal (all-normal) or Gaussian-copula NORTA (non-normal marginals)
Asymmetric normal uses two-piece scaling; uniform/triangular use [-tol_minus,+tol_plus]
Cp/Cpk/Ppk are simulated design-stage indices from overall MC mean/σ — not measured in-control SPC
Sobol requires independent inputs; for this linear stack Si=STi=analytic variance shares
Shapley variance attribution supports correlation; exact for d≤12, permutation estimate for d>12
Under NORTA, analytic σ uses Cov≈ρ·σi·σj (latent ρ); prefer Monte Carlo σ
Shared query must encode noms/sense; legacy tol1/tol2 alone is error-only (nominals 0)
Not full GD&T / 3-D geometry
MCP/agent input schema is canonical (no legacy field aliases); REST still accepts aliases
calculation_fingerprint is SHA-256; calculation_short_id is FNV-1a32 for UI only
MCP execute/inspect default detail_level=summary; pass full for histogram/Sobol/Shapley/contributors
Agent correlations use named pairs {a,b,rho} only (no i/j indexes)
Agent tolerances: half_tolerance OR both tol_plus+tol_minus (no single-sided agent form)

Sources

Standards and references supporting this tool specification. Methods are listed separately — they are algorithms, not bibliographic sources.

NIST IR 6223 — Design for Tolerance of Electro-Mechanical Assemblies — Monte Carlo for assembly tolerance analysis
Supports: Monte Carlo for assembly tolerance and functional requirements
ASME Y14.5 — Dimensioning and Tolerancing — Dimensional tolerancing semantics
Supports: ± and limit tolerancing language background
NIST Engineering Statistics Handbook — Process Capability — 6.1.6 What is Process Capability?
Supports: Distinguishes simulated design indices from measured SPC Cp/Cpk
Statistical tolerance analysis practice — RSS, correlation, sensitivity, capability
Supports: Stack-up, Spearman ranking, design-stage capability

Legacy published checks

Golden and boundary cases from the legacy Evidence JSON. CVP property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the Manifest — including SKIP when a suite has no vectors.

ID	Kind	Status	Detail
`mc`	golden	pass	Expected std=0.07431402402418098 · std_analytic=0.07453559924999299 · Actual n=2 · mode=monte_carlo · profile=basic · N=2000 · seed=42 · k_sigma=3 · correlated=false · sensitivity_method=spearman
`bad-N`	boundary	pass	Expected VALUE_OUT_OF_RANGE · Actual VALUE_OUT_OF_RANGE
`empty`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`seeded`	golden	pass	Expected mean=0.00027942046066928717 · Actual n=2 · mode=monte_carlo · profile=basic · N=2000 · seed=42 · k_sigma=3 · correlated=false · sensitivity_method=spearman
`canonical`	golden	pass	Expected std=0.07431402402418098 · Actual n=2 · mode=monte_carlo · profile=basic · N=2000 · seed=42 · k_sigma=3 · correlated=false · sensitivity_method=spearman
`gap-yield`	golden	pass	Expected stack_nom=5 · yield=0.99285 · Actual n=2 · mode=monte_carlo · profile=dimensional · N=20000 · seed=42 · k_sigma=3 · correlated=false · sensitivity_method=spearman
`asym-uniform`	golden	pass	Expected stack_dist_mean=0.075 · std_analytic=0.07216878364870323 · Actual n=1 · mode=monte_carlo · profile=dimensional · N=10000 · seed=2 · k_sigma=3 · correlated=false · sensitivity_method=spearman
`boundary-mc`	boundary	pass	Expected std=0.07431402402418098 · std_analytic=0.07453559924999299 · stack_nom=0 · Actual n=2 · mode=monte_carlo · profile=basic · N=2000 · seed=42 · k_sigma=3 · correlated=false · sensitivity_method=spearman
`boundary-mc-canonical`	boundary	pass	Expected n=2 · std=0.07431402402418098 · Actual n=2 · mode=monte_carlo · profile=basic · N=2000 · seed=42 · k_sigma=3 · correlated=false · sensitivity_method=spearman
`boundary-mc-gap`	boundary	pass	Expected stack_nom=5 · std_analytic=0.07453559924999299 · yield=0.99285 · Cp=0.8983981967900371 · Actual n=2 · mode=monte_carlo · profile=dimensional · N=20000 · seed=42 · k_sigma=3 · correlated=false · sensitivity_method=spearman
`boundary-mc-corr`	boundary	pass	Expected std_analytic=0.17320508075688773 · correlated=true · Actual n=2 · mode=monte_carlo · profile=dimensional · N=2000 · seed=3 · k_sigma=3 · correlated=true · correlation_model=two_piece_normal
`boundary-mc-shift`	boundary	pass	Expected stack_nom=5 · stack_shift=0.05 · stack_center=5.05 · Actual n=2 · mode=monte_carlo · profile=dimensional · N=500 · seed=1 · k_sigma=3 · correlated=false · sensitivity_method=spearman
`boundary-mc-corr-uniform`	boundary	pass	Expected correlated=true · correlation_model=gaussian_copula_norta · Actual n=2 · mode=monte_carlo · profile=dimensional · N=2000 · seed=1 · k_sigma=3 · correlated=true · correlation_model=gaussian_copula_norta
`boundary-mc-uniform`	boundary	pass	Expected n=1 · std_analytic=0.17320508075688773 · Actual n=1 · mode=monte_carlo · profile=basic · N=2000 · seed=1 · k_sigma=3 · correlated=false · sensitivity_method=spearman
`boundary-mc-one`	boundary	pass	Expected n=1 · std_analytic=0.1 · Actual n=1 · mode=monte_carlo · profile=basic · N=1000 · seed=7 · k_sigma=3 · correlated=false · sensitivity_method=spearman
`boundary-mc-ten`	boundary	pass	Expected n=10 · std_analytic=0.10540925533894598 · Actual n=10 · mode=monte_carlo · profile=basic · N=500 · seed=1 · k_sigma=3 · correlated=false · sensitivity_method=spearman
`boundary-mc-k6`	boundary	pass	Expected std_analytic=0.1 · k_sigma=6 · Actual n=1 · mode=monte_carlo · profile=basic · N=500 · seed=1 · k_sigma=6 · correlated=false · sensitivity_method=spearman
`boundary-mc-zero-pad`	boundary	pass	Expected n=3 · std_analytic=0.07453559924999299 · stack_worst=0.3 · Actual n=3 · mode=monte_carlo · profile=basic · N=500 · seed=3 · k_sigma=3 · correlated=false · sensitivity_method=spearman
`boundary-mc-N-hi`	boundary	pass	Expected VALUE_OUT_OF_RANGE · Actual VALUE_OUT_OF_RANGE
`boundary-mc-empty`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`boundary-mc-k-bad`	boundary	pass	Expected VALUE_MUST_BE_POSITIVE · Actual VALUE_MUST_BE_POSITIVE
`boundary-mc-usl-lsl`	boundary	pass	Expected VALUE_OUT_OF_RANGE · Actual VALUE_OUT_OF_RANGE
`boundary-mc-asym-uniform`	boundary	pass	Expected stack_dist_mean=0.075 · std_analytic=0.07216878364870323 · sensitivity_method=spearman · Actual n=1 · mode=monte_carlo · profile=dimensional · N=10000 · seed=2 · k_sigma=3 · correlated=false · sensitivity_method=spearman
`boundary-mc-sens-pearson`	boundary	pass	Expected sensitivity_method=pearson · Actual n=2 · mode=monte_carlo · profile=basic · N=2000 · seed=42 · k_sigma=3 · correlated=false · sensitivity_method=pearson
`boundary-mc-sens-bad`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`boundary-mc-sobol-corr`	boundary	pass	Expected SOBOL_REQUIRES_INDEPENDENT_INPUTS · Actual SOBOL_REQUIRES_INDEPENDENT_INPUTS
`boundary-mc-sobol`	boundary	pass	Expected sensitivity_method=sobol · Actual n=2 · mode=monte_carlo · profile=basic · N=500 · seed=1 · k_sigma=3 · correlated=false · sensitivity_method=sobol
`boundary-mc-shapley`	boundary	pass	Expected sensitivity_method=shapley · Actual n=2 · mode=monte_carlo · profile=basic · N=500 · seed=1 · k_sigma=3 · correlated=false · sensitivity_method=shapley
`boundary-mc-shapley-corr`	boundary	pass	Expected sensitivity_method=shapley · correlated=true · Actual n=2 · mode=monte_carlo · profile=dimensional · N=500 · seed=1 · k_sigma=3 · correlated=true · correlation_model=two_piece_normal
`boundary-mc-spec-mismatch`	boundary	pass	Expected stack_center=0 · yield=0 · capability_basis=simulated_monte_carlo · Actual n=2 · mode=monte_carlo · profile=dimensional · N=500 · seed=1 · k_sigma=3 · correlated=false · sensitivity_method=spearman
`boundary-mc-yield-extreme`	boundary	pass	Expected yield=0 · Actual n=2 · mode=monte_carlo · profile=dimensional · N=500 · seed=1 · k_sigma=3 · correlated=false · sensitivity_method=spearman
`property-seeded`	property	pass	deterministic
`property-std`	property	pass	std
`property-analytic`	property	pass	σ_analytic = √Σ(T/k)²
`property-mc-near-analytic`	property	pass	N=2000 within 1% of analytic
`property-canonical`	property	pass	tolerances[] ≡ tol1/tol2
`property-permute-analytic`	property	pass	order-invariant analytic
`property-scale-analytic`	property	pass	homogeneous ×2
`property-k1`	property	pass	k=1 → σ=√ΣT²
`property-all-zero`	property	pass	all-zero → σ=0
`property-seed-differs`	property	pass	different seed → different sample
`property-convergence`	property	pass	larger N closer to analytic
`property-rng-meta`	property	pass	PRNG lock
`property-central95`	property	pass	percentile ordering
`property-stack-rss`	property	pass	stack_rss = k·σ_analytic
`property-100-tols`	property	pass	100 tolerances
`property-gap-nom`	property	pass	Gap A−B nominal+σ
`property-yield`	property	pass	yield+Cp≥Cpk
`property-corr-analytic`	property	pass	ρ=0.5 analytic σ = √(σ₁²+σ₂²+2ρσ₁σ₂)
`property-corr-mc-near-analytic`	property	pass	ρ=0.5 MC σ near analytic
`property-mean-shift`	property	pass	mean_shift moves center
`property-sense-alias`	property	pass	sense/direction aliases
`property-uniform`	property	pass	uniform σ = T/√3
`property-triangular`	property	pass	triangular σ = T/√6
`property-asym-mean`	property	pass	asymmetric uniform E[ε]=(+−)/2
`property-sensitivity`	property	pass	Spearman \|ρ\|≤1
`property-convergence-meta`	property	pass	convergence checkpoints
`property-pearson`	property	pass	Pearson sensitivity lock
`property-spec-mismatch-warn`	property	pass	SPEC_CENTER_MISMATCH when center outside LSL/USL
`property-gap-no-mismatch`	property	pass	aligned gap stack has no SPEC_CENTER_MISMATCH
`property-yield-extreme-warn`	property	pass	YIELD_SAMPLING_EXTREME + rule of three when 0 passes
`property-fingerprint`	property	pass	SHA-256 calculation_fingerprint + FNV short_id lock
`property-sobol-exact`	property	pass	Sobol Si=STi=variance share
`property-shapley-indep`	property	pass	Shapley independent = Sobol shares
`property-shapley-corr`	property	pass	Shapley correlated shares sum≈1
`property-norta`	property	pass	NORTA uniform+ρ · MC σ near analytic approx
`property-share-url-noms`	property	pass	Shared URL noms/sense → gap yield + Wilson CI
`property-legacy-tol-nom0`	property	pass	Legacy tol1/tol2+spec without noms → nom=0 (no client invention)
`property-parity-fingerprint`	property	pass	Canonical tolerances[] ↔ legacy query inputs → same fingerprint
`property-fingerprint-stable`	property	pass	Identical request → identical SHA-256 fingerprint
`property-mcp-summary-fields`	property	pass	Summary contract fields present on engine result