**Bill Spath**

I agree with your concerns. In this particular case, the rectangular distribution is larger than the normal distribution that it is being combined with. However when one convolves distributions the central limits theorem communicates that the distribution can be approximated as normal (See GUM G.2.1). The resulting convolved distribution would somewhat resemble a rectangular distribution, but not exactly, it would also be rounding off to resemble a normal distribution as well. Now the question at hand would be, which coverage factor to choose? We have three choices here. We could select k=1.65 if we assume that it more closely resembles rectangular. We can select 2 if we assume that it more closely resembles normal. Lastly, we can do a monte-carlo simulation and determine a more precise coverage factor.

Let’s analyze the consequences of this real example that you provided. The combined uncertainty is 28.99 mA. If you assumed rectangular, the expanded uncertainty is 47.84 mA. If we assume normal, then the expanded uncertainty is 57.99 mA.

Now recall that the resolution of the measurement was 0.1 A in the example. This means that the uncertainty should not be reported with a value less than the least significant digit. If the measured value was say, 99.9 mA, the uncertainty should not be reported either as 0.058mA nor as 0.048 mA, clearly both of these results are much less than the resolution of the device. General metrology practice reports uncertainty with no more than two significant digits, and not more than one digit past the least significant digit of the measurement, so with our example we would be reporting a measured value of 99.9 mA with an uncertainty of 0.06 mA or 99.9 mA with an uncertainty of 0.05 mA. The difference in the reported uncertainty is less than the resolution of the reading. The relative difference in the reported uncertainties is on the order of 0.01%, and to infer that you have knowledge of the estimate of uncertainty to this level is not a good practice.

In summary, you could have chosen either a rectangular distribution, or a normal distribution, but in the end, the difference is insignificant.

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