Tolerance Stack-Up: Worst Case, RSS & Monte Carlo | MechConcepts
Dimensional Analysis Tool

Tolerance Stack-Up Calculator

Worst Case, RSS & Monte Carlo analysis for 1D dimensional chains

01
Target Specification
Define assembly requirement (gap, clearance, or interference)
How Stack-Up Works
Each part has manufacturing tolerance. When assembled, variations accumulate. This calculator predicts final assembly variation using deterministic (Worst Case) and statistical (RSS / Monte Carlo) methods.
02
Tolerance Chain
Dimensions that affect final assembly (+ increases gap, – decreases gap)
#Nominal (mm)± Tol (mm)DistributionDirection
03
Analysis Results
Worst Case
100% safe. Conservative, used for safety-critical assemblies.
RSS (Root Sum Square)
Statistical, 99.73% yield if normal & in control.
Monte Carlo
10k simulations, handles mixed distributions.
WC Total Variation (±)
—mm
WC Maximum Assembly
—mm
WC Minimum Assembly
—mm
Worst Case
T_total = Σ|T_i|    Assembly range = Nominal_sum ± T_total
RSS Variation (±3σ)
—mm
RSS Max Assembly
—mm
RSS Min Assembly
—mm
RSS
T_RSS = √(Σ T_i²)   →   ±3σ range = nominal_sum ± T_RSS
MC Mean Assembly
—mm
Std Deviation (σ)
—mm
Process Capability Cpk
—
Pass Rate
—
> USL Failures
—
< LSL Failures
—
Monte Carlo Simulation
10,000 random assemblies using each dimension’s distribution (Normal, Uniform, Triangular). Pass rate reflects real-world yield.
Add dimensions to see recommendation
04
Method Selection Guide
✓
Worst Case — Safety–critical (brakes, aerospace). 100% pass but costly.
✓
RSS — High-volume production with SPC, Cpk≥1.33. 99.73% yield.
!
Monte Carlo — Mixed distributions, non-normal processes, validation of RSS.

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