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Tolerance Stack-Up Analysis

Statistical tolerance analysis for mechanical assemblies

Stack-Up Target

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User:

Get Started with Templates

Gap — Target ToleranceA-B (±0.025)#1B-C (±0.025)#2C-D (±0.025)#3D-E (±0.025)#4E-F (±0.025)#5F-G (±0.025)#6G-Aʼ (±0.025)#7ABCDEFGAʼAAʼ
Block widths scaled to tolerance magnitude
Features

For a two-part stack-up, assume shared datums and simply add both feature tolerance analyses.

#FromToMfg ProcessNominal (mm)+ Tol (mm)− Tol (mm)Dir
1
A:
B:
2
B:
C:
3
C:
D:
4
D:
E:
5
E:
F:
6
F:
G:
7
G:
Aʼ:

All features assume a normal (Gaussian) distribution for RSS and Monte Carlo analysis. This is standard practice because manufacturing dimensions follow a bell curve around the nominal per the Central Limit Theorem.

Recommendation: Use RSS

With 7 contributors, RSS analysis is a reasonable approach for production scenarios. Use worst-case only for safety-critical or low-volume applications where 100% conformance is required.

RSS assumes independent, normally-distributed feature dimensions. Verify this with process capability data (Cpk ≥ 1.33). For critical assemblies — medical, aerospace, or safety-related — worst-case is the conservative, industry-accepted default.

Results

Worst Case

+0.175

−0.175

Sum of all tolerances (mm)

RSS (4σ)

+0.066

−0.066

Root Sum Square (mm)

DPPM

Set target to calculate

Defective parts per million

Yield

Set target to calculate

Expected manufacturing yield

Worst Case vs RSS Comparison

RSS is 62% tighter than worst case

Worst Case
0.175
RSS (4σ)
0.066

Sensitivity Analysis

Each feature's percentage contribution to total RSS variance. Focus design effort on the top contributors.

#1 (0.025 mm)14.3%#2 (0.025 mm)14.3%#3 (0.025 mm)14.3%#4 (0.025 mm)14.3%#5 (0.025 mm)14.3%#6 (0.025 mm)14.3%#7 (0.025 mm)14.3%
≥40% — Critical 25–39% — High 10–24% — Moderate <10% — Low

Tolerance Allocation

Reverse-solve: given a target tolerance and desired yield, compute what each feature's tolerance should be.

Set a target tolerance above to calculate allocation.

Monte Carlo Simulation

Click “Run” to simulate 1M random assemblies and visualize the stack-up distribution.

Optional: Upload Historical Data

Upload an Excel (.xlsx) or Numbers file with at least 500 rows for reliable results. Format: first row must be column headers 1, 2, 3, ... matching the number of features (7). Each column contains measured values in mm.

File units:
Data contains:

Select a data type above to enable file upload.

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References & Resources

Tolerance Analysis Theory

Monte Carlo Simulation

RSS assumes each feature tolerance represents a ±4σ distribution (99.9937% coverage).

DPPM and yield are based on the RSS stack-up compared to the target tolerance.