English: In relative terms, this is: ▪ u2rel (Mct) = (1/Nt)2 [(t -ac)/(t -at)]2 { [c/(c-ac)]2 u2(Dt) + CM’Q [(M’-at)/(M’-ac)]2 u2(M’c) ▪ + [CM’P M’c(at-ac)/(M’-ac)2]2u2(M’) + [Mct (at-ac)/(t-ac)2]2 u2(t) ▪ + [(Mct /(t-ac)) - (CM’P M’c /(M’-ac))] 2 u2(at) } ▪ ▪ u2rel (Mct) = [(t -ac)/(t -at)]2 {[c/(c-ac)]2(1/Nt)2u2(Dt) + CM’Q(1/Nt)2[(M’-at)/(M’-ac)]2 u2(M’c) + (CM’P M’c/Nt)2 [(at-ac)/(M’-ac)2] 2 u2(M’) + (Mct/Nt)2 [ (at-ac)/(t-ac)2] 2 u2(t) ▪ + [(Mct /Nt(t-ac)) - (CM’P M’c /Nt(M’-ac))] 2 u2(at) } Since (CM’PMc’)/Nt 1 and Mct/Nt 1, we have: u2rel (Mct) [(t -ac)/(t -at)]2 {[c/(c-ac)]2(1/Nt)2u2(Dt) + CM’Q(1/Nt)2[(M’-at)/(M’-ac)]2 u2(M’c) +[(at-ac)/(M’-ac)2]2u2(M’)+[(at-ac)/(t-ac)2]2u2(t) +[(1/(t-ac))-(1/(M’-ac))]2u2(at)} ▪ If at ac, we have: ▪ u2rel (Mct) [c/(c-ac)]2(1/Nt)2u2(Dt) + (CM’P/Nt)2 u2(M’c) +[(1/(t-ac))-(1/(M’-ac))]2u2(at) Back to top ▪ ▪  The combined variance associated with the determination of the conventional mass value of a test mass when using a series of intercomparisons is: ▪ ▪ (1.2.2.2) ▪ u2(Mct) = [(t-ac)/(t-at)] 2 { [c/(c-ac)]2 u2(Dt) + CM’Q [(M’-at)/(M’-ac)] 2 u2(M’c) ▪ + [Mct (at-ac)/(t-ac)2] 2 u2(t) + [(Mct /(t-ac)) - (CM’P M’c /(M’-ac))] 2 u2(at) } ▪ ▪ where all terms are expressed in the same unit of mass ▪ ▪ (1.2.2.2_app.) approximate equation, if at = ac ▪ u2 (Mct) [c/(c-ac)]2 u2(Dt) + CM’Q u2(M’c) + [(Mct /(t-ac)) - (CM’P M’c /(M’-ac))] 2 u2(at) ▪ ▪ (1.2.2.2_app rel.) approximate equation (relative terms) ▪ u2rel (Mct) [c/(c-ac)]2(1/Nt)2u2(Dt) + (CM’P/Nt)2 u2(M’c) +[(1/(t-ac))-(1/(M’-ac))]2u2(at) ▪ ▪ where u2(Dt) is equal to: ▪ ▪ ▪ ▪ where ▪ ▪ ▪ ▪ ▪ ▪ u (Mct) = combined standard uncertainty of the conventional mass of test mass t (expressed in same units as u(Dt)) ▪ urel (Mct) = relative combined standard uncertainty of the conventional mass of test mass t (dimensionless) ▪ Nt = nominal value of the test mass (expressed in same units as u(Dt) and u(McR’) ▪ CM’Q = the coefficient in the Q matrix for mass M’ along the row corresponding to mass t . See section 3.5 ▪ u(Mc’) = combined standard uncertainty of the conventional mass of reference (lead weight) (expressed in same units as u(Dt) and Nt).
French: En termes relatifs, il s'agit de : ▪ u2rel (Mct) = (1/Nt)2 [(t -ac)/(t -at)]2 { [c/(c-ac)]2 u2(Dt) + CM’Q [(M’-at)/(M’-ac)]2 u2(M’c) ▪ + [CM’P M’c(at-ac)/(M’-ac)2]2u2(M’) + [Mct (at-ac)/(t-ac)2]2 u2(t) ▪ + [(Mct /(t-ac)) - (CM’P M’c /(M’-ac))] 2 u2(at) } ▪ ▪ u2rel (Mct) = [(t -ac)/(t -at)]2 {[c/(c-ac)]2(1/Nt)2u2(Dt) + CM’Q(1/Nt)2[(M’-at)/(M’-ac)]2 u2(M’c) + (CM’P M’c/Nt)2 [(at-ac)/(M’-ac)2] 2 u2(M’) + (Mct/Nt)2 [ (at-ac)/(t-ac)2] 2 u2(t) ▪ + [(Mct /Nt(t-ac)) - (CM’P M’c /Nt(M’-ac))] 2 u2(at) } Vu que (CM’PMc’)/Nt 1 and Mct/Nt 1, we have: u2rel (Mct) [(t -ac)/(t -at)]2 {[c/(c-ac)]2(1/Nt)2u2(Dt) + CM’Q(1/Nt)2[(M’-at)/(M’-ac)]2 u2(M’c) +[(at-ac)/(M’-ac)2]2u2(M’)+[(at-ac)/(t-ac)2]2u2(t) +[(1/(t-ac))-(1/(M’-ac))]2u2(at)} ▪ Si at ac, we have: ▪ u2rel (Mct) [c/(c-ac)]2(1/Nt)2u2(Dt) + (CM’P/Nt)2 u2(M’c) +[(1/(t-ac))-(1/(M’-ac))]2u2(at) Haut de la page ▪ ▪  La variance combinée associée à la détermination de la valeur de la masse conventionnelle pour une masse d’essai lorsqu’on utilise une série d’intercomparaisons est : ▪ ▪ (1.2.2.2) ▪ u2(Mct) = [(t-ac)/(t-at)] 2 { [c/(c-ac)]2 u2(Dt) + CM’Q [(M’-at)/(M’-ac)] 2 u2(M’c) ▪ + [Mct (at-ac)/(t-ac)2] 2 u2(t) + [(Mct /(t-ac)) - (CM’P M’c /(M’-ac))] 2 u2(at) } ▪ ▪ où tous les termes sont exprimés dans la même unité de masse ▪ ▪ (1.2.2.2_app.) équation approximation, si at = ac ▪ u2 (Mct) [c/(c-ac)]2 u2(Dt) + CM’Q u2(M’c) + [(Mct /(t-ac)) - (CM’P M’c /(M’-ac))] 2 u2(at) ▪ ▪ (1.2.2.2_app rel.) équation d'approximation (termes relatifs) ▪ u2rel (Mct) [c/(c-ac)]2(1/Nt)2u2(Dt) + (CM’P/Nt)2 u2(M’c) +[(1/(t-ac))-(1/(M’-ac))]2u2(at) ▪ ▪ où u2(Dt) est égal à: ▪ ▪ ▪ ▪ où ▪ ▪ ▪ ▪ ▪ ▪ u (Mct) = incertitude-type combinée de la masse conventionnelle de la masse d’essai t (exprimée dans la même unité que u(Dt)) ▪ urel (Mct) = incertitude-type combinée relative de la masse conventionnelle de la masse d’essai t (sans dimension) ▪ Nt = valeur nominale de la masse d’essai (exprimée dans la même unité que u(Dt) et u(McR’) ▪ CM’Q = coefficient de la matrice Q pour la masse M’ le long de la rangée correspondant à la masse t. Voir section 3.5 ▪ u(Mc’) = incertitude-type combinée de la masse conventionnelle de la référence (poids connu) (exprimée dans la même unité que u(Dt) et Nt).