varmodel_band_k — SPC variation op

• データ種: なし → table(引数だけで決まる op —— 画像やデータの入力を取らない)

• 呼び出し: import fullseye as fs; fs.ledger.varmodel_band_k(n=20, far=0.001, spread='std', df_prior=None) (実装を直接呼ぶなら import varmodel; varmodel.varmodel_band_k(n=20, far=0.001, spread='std', df_prior=None)、台帳から引くなら opsspc.get("varmodel_band_k"))

使い方

Half-width k (in spread units) of the tolerance band for a declared two-sided per-pixel false-alarm rate (table).

A new good pixel x is flagged when |x - center| > k * spread. Under per-pixel independent normal good samples:

• std: (x - mean)/(s * sqrt(1+1/n)) ~ t_{n-1} so k = t_{n-1}^-1(1 - far/2) * sqrt(1+1/n).

• pooled: one variance pooled over many pixels (degrees of freedom df_prior; None = infinite) → normal quantile.

• moderated: empirical-Bayes shrunk variance with df_prior = d0 prior degrees of freedom (Smyth 2004) → t_{n-1+d0}.

• mad: median / MAD centre and spread → no closed form, but the ratio is a pivot, so k is a Monte-Carlo quantile that depends on (n, far) only (fixed seed; mc_far_rel_se is the relative standard error of the achieved rate). Needs n >= 5 and far >= 1e-3.

The threshold comes from the distribution, never from test defects. Returns k, df (0 for mad: no t quantile is involved), far, n, spread, source, mc_far_rel_se.

Raises ValueError for n < 2 (mad: n < 5), far outside [1e-9, 0.5), an unknown spread or a non-positive df_prior.

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)

• (まだありません)

型が繋がる次の op(table を入力に取れる)

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

同カテゴリ(variation)

varmodel_alignment · varmodel_fit · varmodel_calibrate · varmodel_score


*Provenance: varmodel.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.