Tolerance stack

Draw the measurement path first

Follow one continuous path between the two surfaces of interest, recording each dimension once. Do not include both an overall dimension and the same component dimensions again. Check that every tolerance describes the intended half-width around its nominal value.

RSS needs a statistical basis

Root-sum-square combines independent variation terms differently from a worst-case sum. Independence and comparable tolerance conventions matter. An RSS range is not automatically a guaranteed fit or a stated yield percentage, particularly when dimensions are correlated or the process is not centered.

Building a signed dimensional chain

If a gap equals an opening minus two inserted parts, enter the opening as a positive contribution and the parts as negative contributions. The nominal sum follows those signs. The worst-case spread adds the magnitudes of the individual tolerance contributions because each dimension can move in the direction that enlarges or closes the gap.

For three independent contributions each represented by a 0.1 mm half-width, worst-case half-width is 0.3 mm and the root-sum-square value is about 0.173 mm. The smaller number is not a promise that all assemblies fit. Statistical interpretation depends on how each tolerance relates to the actual distribution and on whether the terms are independent. Dimensions made in one setup or controlled by a shared datum can be correlated. A closed dimensional loop can also accidentally count the same physical variation twice. Sketch the chain, identify the measured endpoints, and remove redundant dimensions before using either result to allocate manufacturing tolerances.

Formula

Worst case sums signed endpoint bounds. RSS standard deviation is √Σ(cᵢσᵢ)².