Statistical and worst-case methods to predict assembly variation
WC stackup adds all tolerances linearly. Total gap = sum of individual tolerances. Use for safety-critical assemblies requiring 100% interchangeability. Drives tightest tolerances and highest cost. Example: three parts with ±0.1, ±0.2, ±0.15 mm → ±0.45 mm.
RSS assumes independent normal distribution. Formula: RSS = sqrt(Σ(tol²)). For high-volume production with SPC. Allows ~40% looser tolerances vs WC. Example: ±0.27 mm for three parts.
Run 10,000+ random samples with defined distributions. Output: assembly gap histogram and Cpk. Best for complex multi-part assemblies with non-linear stackup. Tools: Python (numpy/scipy), Minitab.
GD&T (ASME Y14.5) defines cylindrical, rectangular or profile tolerance zones. Position at MMC gives bonus tolerance. Profile controls form, orientation and location. Virtual condition = worst-case boundary.
Floating: position tol = clearance/2. Fixed: position tol = (clearance - major dia)/2. Account for datum shift. Use RSS/Monte Carlo for multi-hole patterns.