Python library for 1D statistical tolerancing analysis and design.
PyPI: https://pypi.org/project/dimstack/
Docs: https://phcreery.github.io/dimstack/
import dimstack as ds
ds.display.mode(ds.display.DisplayMode.RICH)
k = 0.25
target_process_sigma = 3
std_dev = 0.036 / target_process_sigma
m1 = dim = ds.dim.Basic(
nom=208,
tol=ds.tol.Bilateral.symmetric(0.036),
name="a",
desc="Shaft",
).review(
distribution=ds.dist.Normal(208 + k * target_process_sigma * std_dev, std_dev),
)
m2 = dim = (
ds.dim.Basic(
nom=-1.75,
tol=ds.tol.Bilateral.unequal(0, 0.06),
name="b",
desc="Retainer ring",
)
.review()
.assume_normal_dist(3)
)
m3 = dim = (
ds.dim.Basic(
nom=-23,
tol=ds.tol.Bilateral.unequal(0, 0.12),
name="c",
desc="Bearing",
)
.review()
.assume_normal_dist(3)
)
m4 = dim = (
ds.dim.Basic(
nom=20,
tol=ds.tol.Bilateral.symmetric(0.026),
name="d",
desc="Bearing Sleeve",
)
.review()
.assume_normal_dist(3)
)
m5 = dim = (
ds.dim.Basic(
nom=-200,
tol=ds.tol.Bilateral.symmetric(0.145),
name="e",
desc="Case",
)
.review()
.assume_normal_dist(3)
)
m6 = ds.dim.Basic(
nom=20,
tol=ds.tol.Bilateral.symmetric(0.026),
name="f",
desc="Bearing Sleeve",
)
m7 = dim = (
ds.dim.Basic(
nom=-23,
tol=ds.tol.Bilateral.unequal(0, 0.12),
name="g",
desc="Bearing",
)
.review()
.assume_normal_dist(3)
)
items = [m1, m2, m3, m4, m5, m7]
stack = ds.dim.ReviewedStack(name="stacks on stacks", dims=items)
stack.to_basic_stack().show()
stack.show()
ds.calc.Closed(stack).show()
ds.calc.WC(stack).show()
ds.calc.RSS(stack).show()
ds.calc.MRSS(stack).show()
designed_for = ds.calc.SixSigma(stack, at=4.5)
designed_for.show()
spec = ds.dim.Requirement("stack spec", "", distribution=designed_for.distribution, LL=0.05, UL=0.8)
spec.show()
ds.plot.StackPlot().add(stack).add(ds.calc.RSS(stack)).show()Returns:
DIMENSION STACK: stacks on stacks
┏━━━━┳━━━━━━┳━━━━━━━━━━━━━━━━┳━━━┳━━━━━━━┳━━━━━━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━┓
┃ ID ┃ Name ┃ Desc. ┃ ± ┃ Nom. ┃ Tol. ┃ Sens. (a) ┃ Abs. Bounds ┃
┡━━━━╇━━━━━━╇━━━━━━━━━━━━━━━━╇━━━╇━━━━━━━╇━━━━━━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━┩
│ 0 │ a │ Shaft │ + │ 208.0 │ ± 0.036 │ 1 │ [207.964, 208.036] │
│ 1 │ b │ Retainer ring │ - │ 1.75 │ +0.06 / +0 │ 1 │ [-1.81, -1.75] │
│ 2 │ c │ Bearing │ - │ 23.0 │ +0.12 / +0 │ 1 │ [-23.12, -23] │
│ 3 │ d │ Bearing Sleeve │ + │ 20.0 │ ± 0.026 │ 1 │ [19.974, 20.026] │
│ 4 │ e │ Case │ - │ 200.0 │ ± 0.145 │ 1 │ [-200.145, -199.855] │
│ 5 │ f │ Bearing Sleeve │ + │ 20.0 │ ± 0.026 │ 1 │ [19.974, 20.026] │
│ 6 │ g │ Bearing │ - │ 23.0 │ +0.12 / +0 │ 1 │ [-23.12, -23] │
└────┴──────┴────────────────┴───┴───────┴────────────────┴───────────┴──────────────────────┘
REVIEWED DIMENSION STACK: stacks on stacks
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━┳━━━━━━┳━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━━━━━━┳━━━━━━━━━━━━┓
┃ Dim. ┃ Dist. ┃ Shift (k) ┃ C_p ┃ C_pk ┃ μ_eff ┃ σ_eff ┃ Eff. Sigma ┃ Yield Prob. ┃ Reject PPM ┃
┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━╇━━━━━━╇━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━━━━━━╇━━━━━━━━━━━━┩
│ 0: a Shaft + 208 ± 0.036 │ Normal Dist. μ=208.009, σ=0.012 │ 0.25 │ 1.0 │ 0.75 │ 208.0 │ 0.016 │ ± 2.25σ │ 98.76871101 │ 12312.89 │
│ 1: b Retainer ring - 1.75 +0.06 / +0 │ Normal Dist. μ=-1.78, σ=0.01 │ 0.0 │ 1.0 │ 1.0 │ -1.78 │ 0.01 │ ± 3.0σ │ 99.73002039 │ 2699.8 │
│ 2: c Bearing - 23 +0.12 / +0 │ Normal Dist. μ=-23.06, σ=0.02 │ 0.0 │ 1.0 │ 1.0 │ -23.06 │ 0.02 │ ± 3.0σ │ 99.73002039 │ 2699.8 │
│ 3: d Bearing Sleeve + 20 ± 0.026 │ Normal Dist. μ=20.0, σ=0.00867 │ 0.0 │ 1.0 │ 1.0 │ 20.0 │ 0.00867 │ ± 3.0σ │ 99.73002039 │ 2699.8 │
│ 4: e Case - 200 ± 0.145 │ Normal Dist. μ=-200.0, σ=0.04833 │ 0.0 │ 1.0 │ 1.0 │ -200.0 │ 0.04833 │ ± 3.0σ │ 99.73002039 │ 2699.8 │
│ 5: f Bearing Sleeve + 20 ± 0.026 │ Normal Dist. μ=20.0, σ=0.00867 │ 0.0 │ 1.0 │ 1.0 │ 20.0 │ 0.00867 │ ± 3.0σ │ 99.73002039 │ 2699.8 │
│ 6: g Bearing - 23 +0.12 / +0 │ Normal Dist. μ=-23.06, σ=0.01 │ 0.0 │ 2.0 │ 2.0 │ -23.06 │ 0.01 │ ± 6.0σ │ 99.9999998 │ 0.0 │
└───────────────────────────────────────────────────┴──────────────────────────────────┴───────────┴─────┴──────┴────────┴─────────┴────────────┴─────────────┴────────────┘
DIMENSION: stacks on stacks - Closed Analysis
┏━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━┳━━━┳━━━━━━┳━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━┓
┃ ID ┃ Name ┃ Desc. ┃ ± ┃ Nom. ┃ Tol. ┃ Sens. (a) ┃ Abs. Bounds ┃
┡━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━╇━━━╇━━━━━━╇━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━┩
│ 7 │ stacks on stacks - Closed Analysis │ │ + │ 0.25 │ +0.233 / -0.533 │ 1 │ [-0.283, 0.483] │
└────┴────────────────────────────────────┴───────┴───┴──────┴─────────────────┴───────────┴─────────────────┘
DIMENSION: stacks on stacks - WC Analysis
┏━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━┳━━━┳━━━━━━┳━━━━━━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━┓
┃ ID ┃ Name ┃ Desc. ┃ ± ┃ Nom. ┃ Tol. ┃ Sens. (a) ┃ Abs. Bounds ┃
┡━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━╇━━━╇━━━━━━╇━━━━━━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━┩
│ 8 │ stacks on stacks - WC Analysis │ │ + │ 0.1 │ ± 0.383 │ 1 │ [-0.283, 0.483] │
└────┴────────────────────────────────┴───────┴───┴──────┴────────────────┴───────────┴─────────────────┘
DIMENSION: stacks on stacks - RSS Analysis
┏━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━┳━━━━━━┳━━━━━━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━┓
┃ ID ┃ Name ┃ Desc. ┃ ± ┃ Nom. ┃ Tol. ┃ Sens. (a) ┃ Abs. Bounds ┃
┡━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━╇━━━━━━╇━━━━━━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━┩
│ 9 │ stacks on stacks - RSS Analysis │ (assuming inputs with Normal Dist. & uniform SD) │ + │ 0.1 │ ± 0.17825 │ 1 │ [-0.07825, 0.27825] │
└────┴─────────────────────────────────┴───────────────────
8744
──────────────────────────────┴───┴──────┴────────────────┴───────────┴─────────────────────┘
DIMENSION: stacks on stacks - MRSS Analysis
┏━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━┳━━━━━━┳━━━━━━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━┓
┃ ID ┃ Name ┃ Desc. ┃ ± ┃ Nom. ┃ Tol. ┃ Sens. (a) ┃ Abs. Bounds ┃
┡━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━╇━━━━━━╇━━━━━━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━┩
│ 10 │ stacks on stacks - MRSS Analysis │ (assuming inputs with Normal Dist. & uniform SD) │ + │ 0.1 │ ± 0.24046 │ 1 │ [-0.14046, 0.34046] │
└────┴──────────────────────────────────┴──────────────────────────────────────────────────┴───┴──────┴────────────────┴───────────┴─────────────────────┘
REVIEWED DIMENSION: stacks on stacks - '6 Sigma' Analysis
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━┳━━━━━━┳━━━━━━━┳━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━━━━━━┳━━━━━━━━━━━━┓
┃ Dim. ┃ Dist. ┃ Shift (k) ┃ C_p ┃ C_pk ┃ μ_eff ┃ σ_eff ┃ Eff. Sigma ┃ Yield Prob. ┃ Reject PPM ┃
┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━╇━━━━━━╇━━━━━━━╇━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━━━━━━╇━━━━━━━━━━━━┩
│ 11: stacks on stacks - '6... + 0.1 ± 0.26016 │ Normal Dist. μ=0.1, σ=0.05781 │ 0.0 │ 1.5 │ 1.5 │ 0.1 │ 0.05781 │ ± 4.5σ │ 99.99932047 │ 6.8 │
└──────────────────────────────────────────────────┴───────────────────────────────┴───────────┴─────┴──────┴───────┴─────────┴────────────┴─────────────┴────────────┘
REQUIREMENT: stack spec
┏━━━━━━━━━━━━┳━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━━━━━━━━┳━━━━━━━━━━━━┓
┃ Name ┃ Desc. ┃ Distribution ┃ Median ┃ Spec. Limits ┃ Yield Prob. ┃ Reject PPM ┃
┡━━━━━━━━━━━━╇━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━━━╇━━━━━━━━━━━━━╇━━━━━━━━━━━━┩
│ stack spec │ │ Normal Dist. μ=0.1, σ=0.05781 │ 0.425 │ [0.05, 0.8] │ 80.64418072 │ 193558.19 │
└────────────┴───────┴───────────────────────────────┴────────┴──────────────┴─────────────┴────────────┘
dimstack works great as a library in a python script, in REPL, or in JupyterLab.
%pip install -q dimstack
uv run python -m unittest
python -m mkdocs build
python -m mkdocs serve
python -m mkdocs gh-deploy
uv run mkdocs build
uv run mkdocs serve
uv run mkdocs gh-deploy
First bump version in pyproject.toml, then
uv build
uv publish
- https://d2t1xqejof9utc.cloudfront.net/files/147765/Dimensioning%20and%20Tolerancing%20Handbook.pdf?1541238602
- http://www.newconceptzdesign.com/stackups/
- https://github.com/slightlynybbled/tol-stack
- https://www.mitcalc.com/doc/tolanalysis1d/help/en/tolanalysis1d.htm
- https://clas.iusb.edu/math-compsci/_prior-thesis/YFeng_thesis.pdf
- https://ris.utwente.nl/ws/portalfiles/portal/6632975/Salomons96computer1.pdf
- https://ris.utwente.nl/ws/files/6632926/Salomons96computer2.pdf