spc_hotelling_t2 — SPC multivariate op

• データ種: matrix → table

• 呼び出し: import fullseye as fs; fs.ledger.spc_hotelling_t2(data, alpha=0.0027, mean=None, cov=None) (実装を直接呼ぶなら import spc; spc.spc_hotelling_t2(data, alpha=0.0027, mean=None, cov=None)、台帳から引くなら opsspc.get("spc_hotelling_t2"))

使い方

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.

参考(サンプルデータ・文献)

• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。

• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。

• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。

実行できる例(この op を実際に呼ぶ検証済みサンプル)

• poc_spc — py -3.11 examples/poc_spc.py

型が繋がる次の op(table を入力に取れる)

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同カテゴリ(multivariate)

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*Provenance: spc.py — SPC operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。*

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.