English: Please note that using the full equation 2.2.A. instead of "g", we have the following derivatives without approximation: ∂g/∂Dt = [(t-ac)/(t-at)] [c/(c-ac)] ∂g/∂mcR = [(t-ac)/(t-at)] [(M’-at)/(M’-ac)] ∂g/∂at = [(t-ac)/(t-at)] [(mct (t-at)/(t-ac)2) - (mcR/(R-ac))] ∂g/∂R = [(t-ac)/(t-at)] [mcR(at- ∂g/∂t = [(t-ac)/(t-at)] [mct (ac-at)/(t-ac)2]  Thus (ucombined(mct))2 ≈ [ 1 × u(mcR) ]2 + [ - (mR/R - mt/t) × (1-(ac/c))-1 × u(at) ]2  + [ - (ac-at) × (1-(ac/c))-1 × u(vt) ]2 + [ (ac -at) × (1-(ac/c))-1 × u(vR) ]2  + [ (1-(ac/c))-1 × u(Dt) ]2  (ucombined(mct))2 ≈ u(mcR)2 + (1-(ac/c))-2{[-(mR/R - mt/t) u(at)]2 + [-(ac-at)u(vt)]2 + [(ac -at)u(vR)]2 + u(Dt)2}  Since (u(vt))2 ≈ (Mvt/Mt)2 u2(t) ≈ (-mt/t2)2 u2(t) and  (u(vR))2 ≈ (MvR/MR)2 u2(R) ≈ (-mR/R2)2 u2(R)  (ucombined(mct))2 ≈ u(mcR)2 + (1-(ac/c))-2 {[-(mR/R - mt/t) u(at)]2 + [-(ac-at)(-mt/t2) u(t) ]2 + [ (ac -at)(-mR/R2) u(R) ]2 + u(Dt)2 }  Again, replacing mt and mR by their equivalence in conventional mass (ucombined(mct))2 ≈ u(mcR)2  + (1-(ac/c))-2 {u(Dt)2} + (1-(ac/c))-2 {- ([mcR R (1-(ac/c))/(R-ac)] /R - [mct t (1-(ac/c))/(t-ac)] /t) u(at) }2 + (1-(ac/c))-2 {-(ac-at)(-[(mct t (1-(ac/c)) /(t-ac)] /t2) u(t) }2  + (1-(ac/c))-2 { (ac -at)(-[(mcR R (1-(ac/c)) /(R-ac)]/R2) u(R)}2  (ucombined(mct))2 ≈ u(mcR)2 + (1-(ac/c))-2 {u(Dt)2} + (1-(ac/c))-2 { (- (1-(ac/c)))2 ( mcR/(R-ac) - mct /(t-ac) )2 u2 (at)  + (1-(ac/c))-2 {(-(1-(ac/c)))2 (ac-at)2 (-[(mct /(t-ac)] /t)2 u2(t) + (1-(ac/c))-2 { (1-(ac/c))2 (ac -at)2 (-[(mcR/(R-ac)]/R)2 u2 (R)  u2(mct) ≈ u2(mcR)+ c2/(c - ac)2 u2(Dt)+ [mcR/(R - ac) - mct/(t - ac)] 2u2(at) + (ac -at)2 [ (mcR 2u2(R))/R2 (R - ac)2 + (mct2 u2(t)) / t2(t - ac)2]  Since (ac -at)2 [ (mcR 2u2(R))/R2 (R - ac)2] should already be included in u2(mR), the combined standard uncertainty for mct expressed in terms of mcR is the square root of the following:   (3.2.A) u2(mct) ≈ u2(mcR)+ c2/(c - ac)2 u2(Dt)+ [mcR/(R - ac) - mct/(t - ac)] 2u2(at) + (ac -at)2 [(mct2 u2(t)) / t2 (t - ac)2] where all terms are expressed in the same unit of mass   Please note that equation 3.2.A without approximation is: u2(mct) = [(t-ac)/(t-at)]2 {[(M’-at)/(M’-ac)]2 u2(mcR)+ c2/(c-ac)2 u2(Dt) + [mcR(at-ac)/(R-ac)2]2 u2(R) + [(mct (t-at)/(t-ac)2) - (mcR/(R-ac))]2 u2(at) + [mct (ac-at)/(t-ac)2]2 u2(t)}  Please also note that u2(Dt) is the base value of the process uncertainty for the nominal value being calibrated or tolerance tested, as obtained with RP-03Field and implicitly includes both variations in the value of "SR" and variations in the indicated values.
French:   Il convient de noter que si on utilise la pleine équation 2.2.A. au lieu de « g », on obtient les dérivées suivantes sans approximation : ∂g/∂Dt = [(t-ac)/(t-at)] [c/(c-ac)] ∂g/∂mcR = [(t-ac)/(t-at)] [(M’-at)/(M’-ac)] ∂g/∂at = [(t-ac)/(t-at)] [(mct (t-at)/(t-ac)2) - (mcR/(R-ac))] ∂g/∂R = [(t-ac)/(t-at)] [mcR(at- ∂g/∂t = [(t-ac)/(t-at)] [mct (ac-at)/(t-ac)2]  Ainsi, (ucombined(mct))2 ≈ [ 1 × u(mcR) ]2 + [ - (mR/R - mt/t) × (1-(ac/c))-1 × u(at) ]2  + [ - (ac-at) × (1-(ac/c))-1 × u(vt) ]2 + [ (ac -at) × (1-(ac/c))-1 × u(vR) ]2  + [ (1-(ac/c))-1 × u(Dt) ]2  (ucombined(mct))2 ≈ u(mcR)2 + (1-(ac/c))-2{[-(mR/R - mt/t) u(at)]2 + [-(ac-at)u(vt)]2 + [(ac -at)u(vR)]2 + u(Dt)2}  Étant donné que (u(vt))2 ≈ (Mvt/Mt)2 u2(t) ≈ (-mt/t2)2 u2(t) and  (u(vR))2 ≈ (MvR/MR)2 u2(R) ≈ (-mR/R2)2 u2(R)  (ucombined(mct))2 ≈ u(mcR)2 + (1-(ac/c))-2 {[-(mR/R - mt/t) u(at)]2 + [-(ac-at)(-mt/t2) u(t) ]2 + [ (ac -at)(-mR/R2) u(R) ]2 + u(Dt)2 }  Encore une fois, en remplaçant mt et mR par leur équivalence en masse conventionnelle  (ucombined(mct))2 ≈ u(mcR)2  + (1-(ac/c))-2 {u(Dt)2} + (1-(ac/c))-2 {- ([mcR R (1-(ac/c))/(R-ac)] /R - [mct t (1-(ac/c))/(t-ac)] /t) u(at) }2 + (1-(ac/c))-2 {-(ac-at)(-[(mct t (1-(ac/c)) /(t-ac)] /t2) u(t) }2  + (1-(ac/c))-2 { (ac -at)(-[(mcR R (1-(ac/c)) /(R-ac)]/R2) u(R)}2  (ucombined(mct))2 ≈ u(mcR)2 + (1-(ac/c))-2 {u(Dt)2} + (1-(ac/c))-2 { (- (1-(ac/c)))2 ( mcR/(R-ac) - mct /(t-ac) )2 u2 (at)  + (1-(ac/c))-2 {(-(1-(ac/c)))2 (ac-at)2 (-[(mct /(t-ac)] /t)2 u2(t) + (1-(ac/c))-2 { (1-(ac/c))2 (ac -at)2 (-[(mcR/(R-ac)]/R)2 u2 (R)  u2(mct) ≈ u2(mcR)+ c2/(c - ac)2 u2(Dt)+ [mcR/(R - ac) - mct/(t - ac)] 2u2(at) + (ac -at)2 [ (mcR 2u2(R))/R2 (R - ac)2 + (mct2 u2(t)) / t2(t - ac)2]  Vu que les termes (ac -at)2 [ (mcR 2u2(R))/R2 (R - ac)2] devraient déjà être compris dans u2(mR), l'incertitude-type combinée de mct exprimée en termes de mcR est la racine carrée de ce qui suit :  (3.2.A) u2(mct) ≈ u2(mcR)+ c2/(c - ac)2 u2(Dt)+ [mcR/(R - ac) - mct/(t - ac)] 2u2(at) + (ac -at)2 [(mct2 u2(t)) / t2 (t - ac)2] où tous les termes sont exprimés dans la même unité de masse