Tolerance stack-up: worst case vs RSS vs Monte Carlo, with a worked example

Theory: adding tolerances

A stack-up adds the dimensions of the parts that form a gap, with a plus sign when they increase the gap and minus when they reduce it.

Worst case guarantees fit for every assembly but often forces expensive tolerances. RSS assumes each tolerance is ±3σ of a centred normal distribution and gives the ±3σ range of the sum. Monte Carlo makes no formula assumption and simulates many assemblies, which also handles uniform distributions.

Step by step

1. Draw the loop from one face of the gap through every part back to the other face.
2. Enter nominal, + and − tolerance and direction for each dimension.
3. Enter the minimum and maximum gap.
4. Read the three results and the contribution chart.

Case study: bearing end float

The end float in a gearbox is formed by the housing depth (+40.00 ± 0.10), the bearing width (−15.00 +0/−0.12), a spacer (−9.80 ± 0.05) and a gear hub (−14.95 ± 0.08, uniform). The float must be 0.05 to 0.50 mm (the Load sample).

• Centred nominal float: 0.31 mm.
• Worst case: 0.02 to 0.60: fails both limits.
• RSS: 0.16 to 0.46: fits.
• Monte Carlo: about 400 PPM outside, mainly because the hub tolerance is uniform.
• Contributions: gear hub 54 %, housing 28 %, bearing 10 %, spacer 7 %.

Tightening the gear hub to ±0.05 or controlling it as a normal, capable process brings the risk well below 50 PPM; tightening the spacer would have no visible effect.

Common mistakes

• Using the nominal of an asymmetric tolerance instead of its centre.
• Applying RSS to dimensions from processes that are not capable or not centred.
• Forgetting a part in the loop, such as a washer or a gasket.

Frequently asked questions