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).
nu_eff = u_c^4 / sum_i (c_i u_i)^4 / nu_i U = k u_c, k = t_{p}(nu_eff)
★ There are 3 exact properties usable as a gate:
• With only 1 component, nu_eff == nu (exact).
• nu_eff >= min_i nu_i always holds. Proof: sum u_i^4/nu_i <= (1/nu_min) sum u_i^4 <= (1/nu_min)(sum u_i^2)^2. If the effective degrees of freedom fall below those of the smallest component, the computation is broken.
• If all degrees of freedom are infinite, k converges to the quantile of the normal distribution (1.959964 at 95 %).
For infinite degrees of freedom (known constants and the like) put numpy.inf.
• 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.