The simplification method applies as long as the errors in the variables are independent.

That is why I am asking the question because this case does not deal with independent quantities.

Please note: If the errors in the variables are independent. 

Otherwise sum all errors in quadrature.

You may need to consider if your partial differentials are proper. See attached.

When all else fails propagate error by Monte Carlo simulation.

If errors are not independent, you should take into account their covariances as shown in the attached document.

Dear Sirs, I am afraid this issue is still intriguing for me. In a very simple case (uncertainty of flow measurement from acc. volume and time measurements), I found this uncertainty analysis (attached pdf) free available in the web, and I first thought it was clearly flawed since V and t are not independent variables: say, the "correct" expression would be V = Q t instead, so that propagation error should be applied to Q and t for they are the "true" two independent variables involved (t for time, arbitrary one; and Q for vol. flow in pump, that depends on pump and tubing configuration). But the post by Mr. Joseph L Alvarez brought again a doubt on this first belief, since, of course, errors in V and t are independent (V: error coming from recipient scale; t: error coming from selected stopwatch). Eventually, is this attached analysis correct? Thank you so much in advance. Best regards, José Ignacio Gómez Cívicos, pH. D., AMICHemE.

José Ignacio Gómez Cívicos

The analysis is correct. The quantity calculated from the measured values is the flow rate, Q. The calculation of Q (Q = V/t) is from the known volume,V, and the measured time, t. There is an error in the knowledge of V and an error in the measurement of t. These errors are independent. The error in V is not influenced by a measurement of t. The error in t is not influenced by a measurement of V.