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Who published Tolerance Stackup?

ashfordeOU (@ashfordeou) published this skill. Their other Agent Skills are listed on their SkillMD profile.

Tolerance Stackup by ashfordeou — Agent Skill

Name: Tolerance Stackup
Author: ashfordeOU

Tolerance Stackup

Use when you must compute the assembly tolerance stack-up from the part tolerances with the worst case and root sum square methods: sum the absolute tolerances for the worst case total, take the root sum square for the statistical total, sum the signed nominals into the assembly nominal dimension, and produce the assembly limits and the dominant variance share. Produces the worst case total, the RSS total, the assembly limits, and the dominant contributor that gate the fit assessment. Trigger: tolerance stack-up, worst case, root sum square, RSS, assembly limits, dominant contributor, nominal dimension.

ashfordeOU 6a5e242 3 files · 10.6 KB Updated Sep 17, 2026

File contents

Tolerance Stack-up (cross-cutting/tolerancing/tolerance-stackup)

Use when the task is assembly tolerance stack-up analysis from the part tolerances: worst case total, root sum square (RSS) total, signed nominal assembly dimension, assembly limits, and the dominant variance contributor.

Domain quick reference

A linear dimension chain combines signed part nominals n_i with direction d_i (plus or minus 1) into the assembly nominal dimension: N = sum_i d_i * n_i.
The worst case stack-up total is the sum of the absolute part tolerances: T_wc = sum_i t_i. Every part at its extreme limit simultaneously; the assembly limits are N +- T_wc.
The statistical (RSS) stack-up total assumes independent, centered part variations: T_rss = sqrt(sum_i t_i**2). RSS is always less than or equal to the worst case total.
The assembly limits are (N - T, N + T) for the chosen total T.
The RSS variance share of part i is 100 * t_i2 / sum_j t_j2; shares sum to 100 and rank the dominant contributor.
Units: any consistent length unit (mm, inch); all parts must share one unit system. Tolerances are bilateral symmetric half-ranges.

Workflow

Collect the part nominals, directions, and tolerances for the chain.
Sum the signed nominals with nominal_total(nominals, directions).
Compute the worst case total with worst_case_total(tolerances).
Compute the statistical total with rss_total(tolerances).
Produce the assembly limits with stackup_limits(nominal, total).
Rank the contributors with rss_shares(tolerances) and report the dominant one before gating the fit assessment.

Pitfalls

Mixing unit systems in one chain: the stack-up is meaningless unless every part shares a unit system; no conversion is performed.
Negative tolerances: physically meaningless; the logic raises ValueError.
Applying RSS to correlated or biased parts: the independent, centered assumption understates the true spread; worst case is the conservative bound.
Mis-signed directions: a subtracted part entered with the wrong sign shifts the nominal by twice its value.
Using the largest tolerance instead of the largest variance share: the share squares the tolerance, so a large tolerance on a small part may still dominate the RSS total.

Behavior contract (gate 3)

The stack-up logic is exercised by the gate 3 contract test: scripts/test_tolerance_stackup.py against scripts/tolerance_stackup_logic.py (stdlib unittest, offline). Run: python3 scripts/test_tolerance_stackup.py

Compliance

Standards referenced, not reproduced: AS9102 (first article inspection) and AS9100 (quality management) frame the characteristic tolerance and inspection context; the worst case and RSS stack-up methods are generic engineering methodology, summary and formulas only per standards-map.yaml.
compliance: STANDARDS-REF, gated: false.

---name: tolerance-stackupdescription: Use when you must compute the assembly tolerance stack-up from the part tolerances with the worst case and root sum square methods: sum the absolute tolerances for the worst case total, take the root sum square for the statistical total, sum the signed nominals into the assembly nominal dimension, and produce the assembly limits and the dominant variance share. Produces the worst case total, the RSS total, the assembly limits, and the dominant contributor that gate the fit assessment. Trigger: tolerance stack-up, worst case, root sum square, RSS, assembly limits, dominant contributor, nominal dimension.license: Apache-2.0---# Tolerance Stack-up (cross-cutting/tolerancing/tolerance-stackup)Use when the task is assembly tolerance stack-up analysis from thepart tolerances: worst case total, root sum square (RSS) total,signed nominal assembly dimension, assembly limits, and the dominantvariance contributor.## Domain quick reference- A linear dimension chain combines signed part nominals n_i with direction d_i (plus or minus 1) into the assembly nominal dimension: N = sum_i d_i * n_i.- The worst case stack-up total is the sum of the absolute part tolerances: T_wc = sum_i t_i. Every part at its extreme limit simultaneously; the assembly limits are N +- T_wc.- The statistical (RSS) stack-up total assumes independent, centered part variations: T_rss = sqrt(sum_i t_i**2). RSS is always less than or equal to the worst case total.- The assembly limits are (N - T, N + T) for the chosen total T.- The RSS variance share of part i is 100 * t_i**2 / sum_j t_j**2; shares sum to 100 and rank the dominant contributor.- Units: any consistent length unit (mm, inch); all parts must share one unit system. Tolerances are bilateral symmetric half-ranges.## Workflow1. Collect the part nominals, directions, and tolerances for the chain.2. Sum the signed nominals with nominal_total(nominals, directions).3. Compute the worst case total with worst_case_total(tolerances).4. Compute the statistical total with rss_total(tolerances).5. Produce the assembly limits with stackup_limits(nominal, total).6. Rank the contributors with rss_shares(tolerances) and report the dominant one before gating the fit assessment.## Pitfalls- Mixing unit systems in one chain: the stack-up is meaningless unless every part shares a unit system; no conversion is performed.- Negative tolerances: physically meaningless; the logic raises ValueError.- Applying RSS to correlated or biased parts: the independent, centered assumption understates the true spread; worst case is the conservative bound.- Mis-signed directions: a subtracted part entered with the wrong sign shifts the nominal by twice its value.- Using the largest tolerance instead of the largest variance share: the share squares the tolerance, so a large tolerance on a small part may still dominate the RSS total.## Behavior contract (gate 3)The stack-up logic is exercised by the gate 3 contract test:scripts/test_tolerance_stackup.py againstscripts/tolerance_stackup_logic.py (stdlib unittest, offline). Run:python3 scripts/test_tolerance_stackup.py## Compliance- Standards referenced, not reproduced: AS9102 (first article inspection) and AS9100 (quality management) frame the characteristic tolerance and inspection context; the worst case and RSS stack-up methods are generic engineering methodology, summary and formulas only per standards-map.yaml.- compliance: STANDARDS-REF, gated: false.

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