Statistical Tolerance Stack-Up (RSS + Monte Carlo Explained)

Lesson 22 of the GD&T Explained series. Worst-case stack-up is conservative; in high-volume production, every part being at its absolute worst simultaneously is statistically almost impossible. This lesson covers Root Sum of Squares (RSS) — the analytic statistical approach — and Monte Carlo simulation — the general-purpose simulation approach. Both give roughly half the stack of worst-case for the same individual tolerances. In this lesson: 00:00 Intro 00:30 RSS formula derived + worked numbers 02:10 Monte Carlo · 10,000 simulated assemblies 03:40 Picking the right method 04:30 Recap + what's next What you'll be able to do after this lesson: • Apply the RSS formula σ_total = √Σσᵢ² to a real stack-up • Interpret a ±3σ RSS result as the 99.7% confidence interval • Understand when Monte Carlo beats RSS (non-normal or skewed distributions) • Recognize the hybrid worst-case / RSS approach used in production • Be ready for Lesson 23: Functional Gauge Design This is part of a 24-lesson series — GD&T Explained. Subscribe and watch in order. Series playlist: [PASTE PLAYLIST URL HERE] Next lesson — Functional Gauge Design with MMC and Virtual Condition.