Linear vs RSS vs averaged
The single most consequential choice in an apportionment isn't the factors — it's which sum you use. Linear gives you much tighter per-component tolerances. RSS is way more permissive. Which is correct depends on whether your error sources are correlated.
A worked example
Four uncorrelated error sources, each allocated equally. dtot = 100 µm.
- Linear: each source gets 25 µm.
- RSS: each source gets 50 µm (√(4·50²) = 100).
- Averaged: 37.5 µm.
The RSS result allows each bearing or rail to have twice the tolerance of the linear one. That's a real cost savings. But if your errors are correlated (same vendor, same thermal environment, same assembly quirk), RSS overstates how much slack you have and your machine will miss spec.
When to use which
- Linear for systematic errors (calibration residuals, thermal gradient offsets) and correlated random errors.
- RSS for truly independent random errors with zero-mean distributions.
- Averaged as a pragmatic hedge when you're unsure — cheap to do, and the tool renders it anyway.
Key insight
You don't have to pick one and hide the others. The apportionment tool shows all three side-by-side. Use linear to bound your worst case, RSS to find the cost-optimal design, and use the gap between them to flag components worth correlating measurements on.