spc_hotelling_t2 — SPC `multivariate` op

• Data kinds: matrix → table

• Call: import fullseye as fs; fs.ledger.spc_hotelling_t2(data, alpha=0.0027, mean=None, cov=None) (to call the implementation directly, import spc; spc.spc_hotelling_t2(data, alpha=0.0027, mean=None, cov=None); from the registry, opsspc.get("spc_hotelling_t2"))

Usage

Multivariate SPC by Hotelling's T² with an F-distributed control limit.

`data is a 2-D array of shape (m, p) — m observations of p`

correlated features. With the sample mean vector `mu and covariance S`

(unless passed in explicitly), each row's statistic is::

T^2_i = (x_i - mu)' S^-1 (x_i - mu)

charted against the phase-II control limit::

UCL = p (m+1)(m-1) / (m (m-p)) * F_{alpha, p, m-p}

at false-alarm rate `alpha` (default 0.0027, the 3-sigma-equivalent). Returns

a dict with the per-row `t2 array, the ucl`, the integer indices

`out_of_control, and in_control. The mean row (x == mu`) has

`T^2 == 0` (pinned in the tests).

Raises `ValueError`: a non-2-D / empty *data*, fewer observations than

features plus one (covariance not invertible), `alpha outside (0, 1)`, a

singular covariance, or non-finite / mislabelled input.

References (sample data, literature)

• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).

• Operator provenance and references — the sources of the research/methods this op family came from.

• The canonical algorithm (author, year) and its uses are named in the family usage guide above.

Runnable examples (verified samples that actually call this op)

• poc_spc — py -3.11 examples/poc_spc.py

Ops the type connects to (they accept `table` as input)

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Same category (`multivariate`)

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*Provenance: spc.py — SPC operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

spc_hotelling_t2 — SPC multivariate op