I've encountered a problem with combining uncertainties for later use in uncertainty propagation formula with some measurements of the same quantity having different uncertainties.
Having made direct voltage and current measurements, I'm trying to indirectly calculate the electrical resistance's uncertainty via the uncertainty propagation method:
$$\mu(R) = \sqrt{\left({\frac{\partial R}{\partial V} \mu(V)}\right)^2 + \left({\frac{\partial R}{\partial I} \mu(I)}\right)^2}$$
I use the following formulas to calculate $\mu(V)$ and $\mu(I)$:
The uncertainties $\mu(V)$ and $\mu(V)$ are calculated by combining the type A and type B uncertainties. For type A I use standard deviation:
$$\mu_A(x) = \sqrt{S_\overline{x}^2}$$
Whereas for type B calibration and investigator uncertainty $\Delta x$ and $\Delta x_e$ are taken into account:
$$\mu_B(x) = \sqrt{\frac{(\Delta x)^2}{3} + \frac{(\Delta x_e)^2}{3}}$$
I know that these two can be joined to form a combined uncertainty of:
$$\mu(x) =\sqrt{S_\overline{x}^2 +\frac{(\Delta x)^2}{3} + \frac{(\Delta x_e)^2}{3}}$$
However, from what I know, such a combination only works when we assume uniform probability distribution and the fact that all uncertainties contribute evenly. In my case, $2/15$ measurements were made on different Voltmeter settings, which means different type B uncertainty for these two values of $V$.
Is there any way to account for the uneven uncertainty distribution? For example, since the probabilities of encountering these uncertainties are disjoint, maybe I can calculate two different type B uncertainties and then combine them in this fashion?
$$\mu(V) =\sqrt{S_\overline{V}^2 + \frac{13}{15} \frac{(\Delta V_1)^2}{3} +\frac{13}{15} \frac{(\Delta V_{1e})^2}{3} + \frac{2}{15} \frac{(\Delta V_2)^2}{3} +\frac{2}{15} \frac{(\Delta V_{2e})^2}{3}}$$
It is worth noting that the above formula is a wild guess rather than a justified calculation. What I'm trying to achieve is to have a well defined $\mu(V)$ to plug into uncertainty propagation formula. I have yet to take a statistics class and all sources that I found assume uniform probability distribution and uncertainty contribution, which is not my case.
Some additional notes:
-I need to specifically use uncertainty propagation formula.
-I cannot in any way redo the measurements or swap them so that they all lie in the same voltmeter range to not have this problem (that's not the point).
-These two measurement cases are bad enough to cause problems but not sufficient to do a separate resistance calculation for their different voltmeter range (only two points, always linear, can't prove Ohm's Law like this)