Tolerance Stack-Up Analyzer

Dimensional Loop — Contributors

Feature	Nominal	± Tol	Dir	Cpk

Requirement nominal (mm)

Allowed assembly ± (mm)

Assign + to dimensions that close the gap, − to those that open it. Click the Dir cell to flip. Each ± tolerance is treated as ±3σ of a centered normal process (the standard RSS assumption); Cpk < 1 widens the effective tolerance.

Results

Monte Carlo — 100,000 assemblies

Variance Contribution

Method notes & formulas

Worst case T_WC = Σ|tᵢ| — guarantees every in-tolerance assembly passes. Use for safety-critical or <10 units.

RSS T_RSS = √(Σtᵢ²) — assembly ±3σ; 99.73% within if centered & normal.

Benderized 1.5·√(Σtᵢ²) — RSS with Bender's 1.5 safety factor (Bender, 1962).

Cpk-corrected tᵢ,eff = tᵢ / Cpkᵢ then RSS — widens the effective spread for low-capability processes (symmetric approximation; a true mean shift is not modeled).

Monte Carlo — 10⁵ centered-normal samples per contributor (σᵢ = tolᵢ/(3·Cpkᵢ)), summed by direction; failure rate read directly from the tails.

Yield % for the statistical methods = 2Φ(T_allow/σ)−1, σ from each method's assembly tolerance.