tolerance-stackup

Worst-case stacking assumes every part goes wrong at once. This samples what dimensions actually do. On my test assembly worst case said fail; 200,000 sampled builds said 125 ppm

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tolstack

Monte Carlo tolerance stack-up analysis for mechanical assemblies. No dependencies beyond the Python standard library.

The problem

You have a chain of dimensions that add up to one gap that has to stay inside a spec. There are three ways to predict that gap:

  • Worst case. Sum the tolerance bands. Assumes every part in the assembly arrives at the wrong end of its band on the same day. Safe, and usually so pessimistic that you buy tolerances you never needed.
  • RSS. Root sum square of the bands. Assumes everything is normal, centred and independent. Closer, but it lies the moment a process runs off-centre or a dimension is uniform.
  • Monte Carlo. Sample each dimension from the distribution it actually has. Slower, and right.

This tool runs all three side by side so the gap between them is visible.

Use

python3 tolstack.py examples/shaft-housing.json
python3 tolstack.py examples/lever-linkage.json -n 500000 --seed 7
python3 tolstack.py examples/shaft-housing.json --csv samples.csv
python3 tolstack.py --selftest

Defining a stack

{
  "name": "Bearing seat clearance",
  "units": "mm",
  "lower": 0.020,
  "upper": 0.180,
  "dimensions": [
    { "name": "housing bore", "nominal": 40.000, "tol": 0.050,
      "direction": 1, "dist": "normal", "sigma_ratio": 3.0 },
    { "name": "bearing od",   "nominal": 39.960, "tol": 0.012,
      "direction": -1, "dist": "normal", "sigma_ratio": 4.0 }
  ]
}
field meaning
nominal centre of the dimension
tol half band, so 40.0 +/- 0.05 is nominal 40.0 and tol 0.05
direction 1 if the dimension opens the gap, -1 if it closes it
dist normal, uniform or triangular
sigma_ratio how many sigma the band covers. 3 gives Cp = 1.0, 4 gives a tighter process
shift mean offset, for a process you know runs off-centre

What it reports

Mean, standard deviation, defects in ppm, yield, Cpk, an ASCII histogram with the spec limits flagged, and a ranked variance contribution table.

That last table is the useful one. Variances add on a linear stack, so each dimension's share of the output variance tells you exactly which single tolerance is worth money to tighten, and which ones you are wasting effort on.

Sample output

Running the bearing example: worst case spans 0.0030 to 0.1970 against a spec of 0.020 to 0.180, so worst case says the design fails. Monte Carlo over 200,000 assemblies gives 125 ppm defective and a Cpk of 1.17. The design is marginal rather than broken, and the housing bore owns 61 percent of the variance, so that is the one dimension to tighten.

Tests

--selftest checks the nominal sum, the worst-case band, the RSS band against a hand calculation, the sampled mean and standard deviation against theory, the uniform standard deviation of tol/sqrt(3), that a mean shift lowers Cpk, and that a fixed seed reproduces exactly.

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