# How does one combine independent repeatability and accuracy uncertainties on the same quantity in a reported uncertainty value?

I have a NIST calibrated photodiode with reported $\pm$2% uncertainty in the calibration. I've interpreted this as the "accuracy uncertainty", though I apologize if my terminology is misleading.

If I measure the same quantity multiple times using this photodiode, I find a standard deviation over $N$ measurements of $\pm$0.5%. I've called this the "repeatability uncertainty".

How can I reconcile these uncertainties in a measurement? What is the standard method of reporting an uncertainty value? Specifically, when the same measured quantity has both an uncertainty in calibration (which may not systematically lie to one side or the other of the mean) and an uncertainty arising to repeatability, how can the uncertainties be utilized to predict the overall uncertainty?

Here are two scenarios:

Scenario I

I use the same measurement device to measure a relative value, e.g. the light intensity in front of and behind an optic. I propose that by not relying on the calibrated value that I can essentially ignore the accuracy uncertainty and report uncertainty as $$\sigma_{measurement} = \sqrt{\sigma_{input}^2+\sigma_{output}^2} = \sqrt{2}\sigma_{input}$$

Scenario II

I characterize a second device (sample) to calibrate its absolute performance against the calibrated reference. Each measurement (calibrated reference and sample) has the same repeatability uncertainty, but the reference to the calibrated values requires dividing once by the values with reported accuracy uncertainty. I am uncertain of how to proceed in determining the overall uncertainty in the measured value of the calibrated reference in this case where $$\mathrm{Value\enspace of\enspace interest} = \frac{I_{\mathrm{sample}}}{I_{\mathrm{{reference}}} * f_{\mathrm{calibration, reference}}}$$

Is it as simple as $$\sigma_{measurement} = \sqrt{\sigma_{\mathrm{sample}}^2+\sigma_{\mathrm{reference}}^2+\sigma_{\mathrm{calibration\enspace factor}}^2} \enspace \enspace \mathrm{?}$$