Engineering Reference

Tolerance stack-up

The accumulation of individual tolerances through an assembly.

Definition

Worst-case analysis adds the tolerances arithmetically and guarantees that any combination of conforming parts assembles. Root-sum-square combines them statistically, giving a much smaller total but accepting that a small percentage of assemblies will be out of tolerance.

The choice is a business decision rather than a mathematical one: worst case for safety-critical and low-volume work, RSS for high-volume production where a small reject rate is cheaper than tight tolerances everywhere.

Common misuse

Applying RSS without confirming the processes are centred and in statistical control. If a process drifts, RSS understates the real variation.

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