dimstack

Python library for 1D statistical tolerancing analysis and design.

PyPI: https://pypi.org/project/dimstack/

Docs: https://phcreery.github.io/dimstack/

Example (MIT Calc Demonstration Analysis)

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] │
└────┴─────────────────────────────────┴──────────────────────────────────────────────────┴───┴──────┴────────────────┴───────────┴─────────────────────┘

                                                       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  │
└────────────┴───────┴───────────────────────────────┴────────┴──────────────┴─────────────┴────────────┘

Usage

dimstack works great as a library in a python script, in REPL, or in JupyterLab.

and Notebook setup

%pip install -q dimstack

Development

Testing

uv run python -m unittest

Documenting

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

Deploying

First bump version in pyproject.toml, then

uv build
uv publish

Acknowledgements

• https://d2t1xqejof9utc.cloudfront.net/files/147765/Dimensioning%20and%20Tolerancing%20Handbook.pdf?1541238602
• http://www.newconceptzdesign.com/stackups/
  • https://web.archive.org/web/20221206235926/http://www.newconceptzdesign.com/tutorial/Tutorial-My_first_stackup.html
• 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