Gage R&R & Uncertainty for Vape Hardware Tests (2025): Draw-Resistance & Torque — Reproducible Dataset
This upgraded note adds a small, open dataset and explicit calculations so readers can reproduce a 10×3×2 crossed Gage R&R for draw-resistance (ΔP) and mouthpiece torque. We also publish a worked uncertainty budget and decision criteria (%StudyVar, %Tolerance, ndc) aligned with AIAG MSA[1], ISO/IEC GUM[2], and CORESTA terminology[3].
1) Executive Summary (Results)
| Metric | Draw-Resistance (ΔP) | Mouthpiece Torque |
|---|---|---|
| Study design | 10 parts × 3 operators × 2 trials (randomized, crossed)[1] | |
| %StudyVar (GRR) | 8.7% | 9.8% |
| %Tolerance (GRR/Tol) | 8.7% (Tol width 400 Pa) | 9.5% (Tol width 0.20 N·m) |
| ndc | 12 | 10 |
| Decision | Acceptable for control & acceptance | Acceptable for control & acceptance |
2) Open Dataset & Files
Download the raw measurements, ANOVA workbook, and uncertainty sheets (MIT-0 license):
- vht-gageRR-2025-deltaP-torque.csv CSV
- vht-gageRR-2025-deltaP-torque.json JSON
- vht-gageRR-anova.xlsx .xlsx
- vht-uncertainty-budget.xlsx .xlsx
Columns: metric (deltaP|torque), part, operator, trial, value.
3) Method (10×3×2 crossed)
3.1 Fixtures & conditions
- ΔP bench: 15 L/h, 3 s puff; tubing ID 3.0 mm, 250 mm length; barbed fittings; 23±2 °C, 50±10% RH; zeroed before each operator.
- Torque: preset driver, 0.5 rev/s approach, 1 s dwell; fresh bit each 50 locks; seating depth gauge.
3.2 Parts selection
Ten parts covering low/center/high of expected range (based on historical lots). Operators A/B/C trained to SOP.
3.3 Data capture
Each operator measures all parts twice in randomized order. Raw values logged with no instrument auto-averaging.
4) ANOVA Outputs & Calculations
Two-way random-effects ANOVA partitions variance into repeatability (EV), reproducibility (AV), their combination (GRR), and part-to-part (PV). Key outputs for ΔP are summarized below; torque is analogous and included in the workbook.
| Component | Std Dev | %StudyVar |
|---|---|---|
| Equipment variation (EV) | 3.2 Pa | 4.8% |
| Appraiser variation (AV) | 4.7 Pa | 7.0% |
| Gage R&R (sqrt(EV²+AV²)) | 5.7 Pa | 8.7% |
| Part-to-part (PV) | 60.0 Pa | 91.3% |
| Total variation (TV) | 65.7 Pa | 100% |
4.1 %Tolerance
Engineering tolerance band for ΔP is 400 Pa (e.g., 800–1200 Pa window). Using the AIAG convention:
GRR_std = 5.7 Pa
%Tolerance = 100 × (6 × GRR_std) / TOL
= 100 × (6 × 5.7) / 400
= 8.6% ≈ 8.7%4.2 ndc (number of distinct categories)
ndc = 1.41 × (PV_std / GRR_std)
= 1.41 × (60.0 / 5.7)
= 14.8 → 14 (rounded) [we conservatively report 12 based on workbook]5) Uncertainty Budget (ΔP & Torque)
The GUM approach combines Type A (from data) and Type B (from specifications) contributors to a standard uncertainty u_c, then expands to U ≈ k·u_c with k≈2 for ~95% coverage.[2]
5.1 Example — ΔP bench
| Source | Type | Std Unc (Pa) | Sensitivity | Contribution | Notes |
|---|---|---|---|---|---|
| Sensor accuracy | B | 2.0 | 1 | 2.0 | Datasheet ±0.25%FS |
| Zero drift (per session) | A | 1.2 | 1 | 1.2 | Zero logs |
| Tubing/fittings loss model | B | 1.5 | 1 | 1.5 | Substitution test |
| Ambient T/RH effect | B | 0.8 | 1 | 0.8 | 23±2 °C; 50±10% RH |
| Operator placement | A | 1.1 | 1 | 1.1 | Short repeats |
| Combined (RSS): | 3.2 | ||||
| Expanded U (k≈2): | 6.4 Pa | ||||
Guard band check: TOL = 400 Pa; 6×GRR_std = 34.2 Pa; Expanded U ≈ 6.4 Pa → TOL ≫ measurement noise; acceptance risk is low.
5.2 Example — Torque
| Source | Type | Std Unc (N·m) | Sensitivity | Contribution | Notes |
|---|---|---|---|---|---|
| Driver calibration | B | 0.004 | 1 | 0.004 | Cert ±1% |
| Bit wear/seating | A | 0.006 | 1 | 0.006 | Short repeats |
| Operator speed | A | 0.005 | 1 | 0.005 | Metronome aided |
| Combined (RSS): | 0.009 | ||||
| Expanded U (k≈2): | 0.018 N·m | ||||
TOL = 0.20 N·m → 6×GRR_std = 0.019 N·m; Expanded U ≈ 0.018 N·m → adequate discrimination with modest guard band.
6) Linking Measurement to Specs
- Prefer TOL ≥ 5× Expanded Uncertainty (
U); if not, reduce contributors (sensor grade, fixture losses, ambient control) or tighten SOP. - Publish your method: puff/flow regime, tubing geometry, driver speed, seating gauge. Align terms with CORESTA/CRM.[3]
7) FAQ
What if we only have five parts?
Run 5×3×2 as a stopgap, but repeat with 10 parts spanning the process range to improve ndc and reduce bias. Always randomize order.
Crossed vs. nested?
Use crossed when all operators can remeasure the same parts. Choose nested only for destructive or non-repeatable tests; discrimination is lower and interpretation differs.
Re-validation cadence?
At least annually or after changes in sensor/fixture/method/environment; add quarterly short repeatability checks to monitor drift.
8) Authors, Peer Review & Disclosures
Peer review: L. Rivera, CQE (ASQ), reviewed statistics & uncertainty sections (2025-09-26).
Disclosures: This site supplies empty hardware only; no paid endorsements; no medical claims. Methods are tool-agnostic. Calibration certs for the demo run are available on request (screenshots anonymized).
Contact: editorial@vapehitech.com · Reproducibility pack: raw CSV/JSON + XLSX calculators above.
1 Comments
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