20180227 - Uncertainty Formulas

Wednesday, 28 February 2018

12:02 AM

$Machine generated alternative text: If the uncertainties are de xarn e endent (based on the same source of uncertain ) the add linearl : Adding or subtracting Multiplying or dividing Using formulae p + h), when the dominant uncertainty is a systematic uncertainty v = I x h x b, where the dominant uncertainty in each is a systematic uncertainty common to l, h, b et O Add absolute uncertainty Ay Ax + Ax 2Ax Ay = Ax, + AP = 2(Al + Ah) Note the plus sign A ractiona /percentage errors Aa Ab Ac Av Al Ah Ab b Use the differentia method2 or test the extreme points. Ay = Ax x f or Ay _ Ax) —Rx — Ax) 2 If the uncertainties are independent (they have different, uncorrelated sources) they add in uadrature: eratlOn Adding or subtracting Multiplying or dividing Using formulae xan-l e et o a so ute uncertainties In qua rature. AZ (Ax) 2 + (Ay)2 AP = 2 (Alf + (Ah)2 Add fractional (percentage) uncertainty in quadrature. Az Ay partla erlvatlve welg te uncertalntles In qua ratur _ Df Ax x Ox z f(x,y) + Ay x (fix.y 4-Ay) — fix.y — Ayl)2 AZ (fix + Ax.y) — fix — Ax.yb)2 To get from a fractional uncertainty to a percentage uncertainty multiply by 100 Beware of the possibility of a turning point between X+Ax and x—Ax, which will cause this method to fail. (e.g. y = sin(x), where x = 100)$