uncertainty op• Data kinds: table → table
• Call: import fullseye as fs; fs.ledger.gum_expanded(table, u='u', sensitivity='sensitivity', dof='dof', level=0.95, correlation=None, estimate=None, lower_bound=None, upper_bound=None) (to call the implementation directly, import spc; spc.gum_expanded(table, u='u', sensitivity='sensitivity', dof='dof', level=0.95, correlation=None, estimate=None, lower_bound=None, upper_bound=None); from the registry, opsspc.get("gum_expanded"))
Welch-Satterthwaite effective degrees of freedom, coverage factor k and expanded uncertainty U (`table`).
> The detailed description below is the original text — the summary and the headings are translated.
nu_eff = u_c^4 / sum_i (c_i u_i)^4 / nu_i U = k u_c, k = t_{p}(nu_eff)
★門にできる厳密な性質が 3 つある:
• 成分が 1 つだけなら `nu_eff == nu`(厳密)。
• `nu_eff >= min_i nu_i` が常に成り立つ。証明は
`sum u_i^4/nu_i <= (1/nu_min) sum u_i^4 <= (1/nu_min)(sum u_i^2)^2`。
有効自由度が最小の成分より小さくなったら計算が壊れている。
• すべての自由度が無限大なら `k` は正規分布の分位点へ収束する
(95 % で 1.959964)。
無限自由度(既知の定数など)は `numpy.inf` を入れる。
• 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.
• poc_measurement_system_analysis — py -3.11 examples/poc_measurement_system_analysis.py
table as input)msa_anova_table · msa_gauge_rr · msa_bias_linearity · msa_attribute_agreement · gum_standard_uncertainty · gum_propagate · gum_monte_carlo · gum_validate
uncertainty)gum_standard_uncertainty · gum_propagate · gum_monte_carlo · gum_validate
*Provenance: spc.py — SPC operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.