Verified calculation capability
1-D Tolerance Analysis Workspace — dimensional Monte Carlo with asymmetric ±tol, correlations (normal or NORTA), Spearman/Pearson/Sobol/Shapley sensitivity, σ convergence, LSL/USL yield, simulated capability, fingerprint, and snapshots. · Engineering · Tolerance
Capability ID engineering.tolerance.monte_carlo · version 1.12.0
Stack
y = Σ c_i · (nom_i + shift_i + ε_i)σ² = Σ (cσ_ε)² + 2 Σ ρ c_i c_j σ_i σ_jCp*=(USL−LSL)/(6σ); Cpk*=min(Cpl,Cpu) — design-stage MC, not SPCCanonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit | Role |
|---|---|---|---|
tolerances | Canonical stack components. y = Σ c·(nominal + ε). | — | input / output |
N | Monte Carlo iterations (default 5000). | — | input / output |
seed | PRNG seed (mulberry32). | — | input / output |
k_sigma | For normal: half_tolerance = k_sigma · σ (default 3). | — | input / output |
LSL | Lower specification limit (optional). | — | input / output |
USL | Upper specification limit (optional). | — | input / output |
unit | Optional display unit (mm, in, …). | — | input / output |
correlations | Optional pairwise correlations by dimension name: [{a,b,rho}]. ρ is Pearson (all-normal) or latent normal (NORTA). | — | input / output |
sensitivity_method | Sensitivity method (default spearman). sobol = exact first-order for independent linear stacks; shapley = variance attribution (supports correlation). | — | input / output |
sobol_N | Optional Saltelli MC cross-check size when sensitivity_method=sobol. | — | input / output |
shapley_N | Optional permutation count when sensitivity_method=shapley and d>12 (exact for d≤12). | — | input / output |
profile | — | — | output |
n | amount of substance | — | output |
tol | — | — | output |
half_tolerances | — | — | output |
stack_nom | Σ cᵢ·nominalᵢ | — | output |
mean | — | — | output |
std | — | — | output |
std_analytic | — | — | output |
std_rel_err | — | — | output |
p025 | — | — | output |
p05 | — | — | output |
p50 | — | — | output |
p95 | — | — | output |
p975 | — | — | output |
p99 | — | — | output |
stack_worst | — | — | output |
stack_rss | — | — | output |
yield | Fraction of samples within spec limits | — | output |
reject_rate | — | — | output |
ppm_below | — | — | output |
ppm_above | — | — | output |
ppm_total | — | — | output |
below_count | — | — | output |
above_count | — | — | output |
in_spec_count | — | — | output |
Cpl | — | — | output |
Cpu | — | — | output |
Ppk | — | — | output |
rng | — | — | output |
histogram | — | — | output |
correlated | — | — | output |
correlation_model | null if independent; two_piece_normal for all-normal joint; gaussian_copula_norta for non-normal/mixed marginals. | — | output |
stack_shift | — | — | output |
stack_center | stack_nom + stack_shift | — | output |
contributors | — | — | output |
Cp | — | — | output |
Cpk | — | — | output |
stack_dist_mean | — | — | output |
convergence | — | — | output |
capability_basis | — | — | output |
capability_normal_equivalent | — | — | output |
simulated_Cp | — | — | output |
simulated_Cpk | — | — | output |
sensitivity_metric | — | — | output |
yield_sampling | — | — | output |
calculation_fingerprint | Audit fingerprint: sha256 of canonical normalized inputs + engine/PRNG lock. | — | output |
calculation_short_id | Short FNV-1a32 id for UI/cache only — not an audit fingerprint. | — | output |
sobol | — | — | output |
shapley | — | — | output |
Declared scope for this capability. Do not use it outside this domain.
Assumptions
Not supported
One numerical check. The calculator page holds worked steps and FAQ.
A=10 +0.1/−0.05, B=5±0.2, LSL=4.8, USL=5.2
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.. Computational verification is defined by CVP. Supplemental domain review (internal) and named expert review are defined by the Review policy and do not by themselves determine CVP conformance.
Human page, REST, and MCP share the same engine and calculation_version.
Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json
and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 8/8.
Human-readable sources plus CVP reference evidence classes.
Sources
Reference evidence classes: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Inspect this capability via same-origin MCP, then call execute_calculation.
curl -sS -X POST 'https://www.calculatorx.com/mcp' \
-H 'Content-Type: application/json' \
-H 'MCP-Protocol-Version: 2026-07-28' \
-H 'Mcp-Method: tools/call' \
-H 'Mcp-Name: inspect_capability' \
-d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"engineering.tolerance.monte_carlo"}}}'
Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.12.0) when reproducibility matters. Full protocol notes: MCP docs.