spc_mt_distance — SPC mt op

• Data kinds: matrix → table

• Call: import fullseye as fs; fs.ledger.spc_mt_distance(data, mean=None, std=None, inv_corr=None, threshold=3.0) (implementation को सीधे call करना हो तो import spc; spc.spc_mt_distance(data, mean=None, std=None, inv_corr=None, threshold=3.0), registry से लेना हो तो opsspc.get("spc_mt_distance"))

उपयोग

observations को MT-method unit space के सापेक्ष score करता है।

> नीचे का विस्तृत विवरण मूल text में है — सारांश और headings का अनुवाद हो चुका है।

data is a 2-D array of shape (m, p). Pass the mean, std and inv_corr from spc_mt_unit_space to score new product against a stored unit space; omit all three and the unit space is built from data itself, which is the training case and makes md_sq_mean land on (m-1)/m.

Each row's distance is MD_i = sqrt(z_i' R^-1 z_i / p) with z_i = (x_i - mean) / std. Rows with MD > threshold are reported in flagged; the rest in inside. Dividing the quadratic form by p is what puts the unit space at 1 regardless of how many features are used, so a threshold carries over when features are added or removed.

Returns a dict with the per-row md and md_sq arrays, flagged, inside, the threshold, md_sq_mean, and n/p.

Relationship to spc_hotelling_t2 (used as the oracle in the tests):

on the standardised matrix the covariance *is* the correlation, so md**2 == t2 / p exactly for the same data.

Raises ValueError: a non-2-D / empty *data*, a non-positive threshold, a unit space given only in part, a mean / std / inv_corr whose shape disagrees with p, a non-positive entry in std, or non-finite input.

संदर्भ (sample data, साहित्य)

• Sample data catalog (DL URL / license) — 2-D के लिए skimage.data (BSD/public) + synthetic, 3-D के लिए real data sources (Stanford/PDS आदि) के DL URL।

• Operators का स्रोत और संदर्भ — इस op family के मूल research/methods के स्रोत।

• Algorithm का मानक स्रोत (लेखक, वर्ष) और उपयोग ऊपर की family usage guide में दिए गए हैं।

चलाए जा सकने वाले उदाहरण (verified samples जो सच में यह op call करते हैं)

• poc_mt_hidden_fault — py -3.11 examples/poc_mt_hidden_fault.py

• poc_spc — py -3.11 examples/poc_spc.py

वे अगले ops जिनसे type जुड़ता है (table को input के रूप में लेते हैं)

msa_anova_table · msa_gauge_rr · msa_bias_linearity · msa_attribute_agreement · gum_standard_uncertainty · gum_propagate · gum_expanded · gum_monte_carlo

इसी category के (mt)

spc_mt_unit_space · spc_mt_sn_ratio


*Provenance: spc.py — SPC operator registry. यह per-op note tools/opdocs.py md से अपने-आप generate होता है (हाथ से edit न करें)।*

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