spc_hotelling_t2 — SPC multivariate op

• 数据种类:matrix → table

• 调用: import fullseye as fs; fs.ledger.spc_hotelling_t2(data, alpha=0.0027, mean=None, cov=None)(要直接调用实现,import spc; spc.spc_hotelling_t2(data, alpha=0.0027, mean=None, cov=None);从台账取用则 opsspc.get("spc_hotelling_t2"))

用法

> 该算子的说明尚无译文,以下照原文给出。

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(示例数据・文献)

• 示例数据目录(下载 URL / 许可证) —— 2-D 用 skimage.data(BSD/公有领域)加合成图,3-D 给出真实数据源(Stanford/PDS 等)的下载 URL。

• 算子来历与参考文献 —— 该算子族所依据的研究/方法出处。

• 算法的正典(作者・年份)与用途见上面的族使用指南。

可运行的示例(实际调用该算子并已验证的样例)

• poc_spc — py -3.11 examples/poc_spc.py

类型可衔接的下一个算子(可接受 table 作为输入)

—

同类别(multivariate)

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*Provenance: spc.py — SPC 算子登记表。本条目由 tools/opdocs.py md 自动生成(请勿手工编辑)。*

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