Each conforming part is merely within its own specification. If several deviations align, assembly clearance may still become negative. Start tolerance analysis from the functional closed loop, identify dimensions that add or subtract clearance, then calculate worst-case or statistical behavior.
Values in this article support engineering screening during design review, RFQ and prototyping. They do not replace formal calculations, material data sheets, qualified procedures or contractual standards.
TWO METHODS
Worst case: T_total=Σ|T_i|, guaranteeing all limit combinations but often conservative. Statistical RSS: T_RSS=√ΣT_i², assuming independent, approximately centered distributions; process shifts, correlation or non-normality can make RSS optimistic. Five independent ±0.20 mm dimensions yield ±1.00 mm worst case and ±0.447 mm RSS. For safety or guaranteed interchangeability, favor worst case or a functional gauge.
PRACTICAL WORKFLOW
1. Draw an assembly section and closed-loop arrows; define the output such as gap, end play or hole mismatch. 2. Include only dimensions actually in the loop, with signs. 3. Calculate nominal margin and limits; where appropriate run Monte Carlo using measured means/standard deviations. 4. Allocate tolerance to the cheapest, most stable and measurable contributors; do not tighten every dimension equally. 5. During validation, mix parts across lots rather than testing matched pairs only.
PROJECT CHECKLIST
Functional loop; datum alignment; worst-case/RSS assumptions; process shifts; temperature; coatings; assembly force; cross-lot interchangeability.