That's a good question. I had the same question 20+ years ago...been doing this a long time. The answer is found within the ISO GUM Section G.2. But to make life a bit easier, I will elaborate and provide you with a PDF used in our training class for Uncertainty Analysis that addresses this topic. But first, let me try to explain what is going on and why you got a goofy result.

Here we go...

With only one contributor of a distribution other than a Normal Distribution, the Central Limit Theorem requirement for use of the Normal Distribution for uncertainty expansion, as per the ISO GUM, has not been met. So the result is goofy. Basically, you are computing the standard deviation of a U-Shaped Distribution and then pretending it magically became a Normal Distribution and expanded it with a k value from the Normal. So instead of 95% containment you have 141%...and since anything above 100% is goofy, the result is obviously WRONG, yet nothing is wrong with the math.

The ISO GUM Method relies heavily on the assumption that you will be combining multiple standard deviations from various distributions, which brings us to the Central Limit Theorem. Basically, it requires three or more standard deviations from any type distribution to magically convolve them into a 'Normal' distribution, of which a k = 2 appropriately provides a containment limit with about 95% level of confidence.

Ok, it's not really magic, but it works like magic. Meaning, a demonstration is in order. So, to assist you in getting a better understanding of this, I am attaching a PDF which is part of our Uncertainty Class materials. In it, I have included screen shots of a Monte Carlo tool (spreadsheet) which is part of the Training Workbook we provide to attendees.

Review the attachment, and the ISO GUM sections discussed. Hopefully this will answer your question and provide you insight regarding how this magic trick works...and sadly, the magic will be gone, but an understanding of what is happening and what is required to make it happen, replaces it. In the screen shots you will see the graphed results of 3 Rectangular Distributions convolving into a Normal, in three different scenarios.

1) All of equal spread (containment limits).

2) Different limits; +/- 0.5, +/- 1.5, +/- 2.5

3) Different limits with one being 5 times bigger than the other two; +/- 0.5, +/- 0.5, +/- 2.5...again all are Rectangular Distributions. But the convolved distribution takes on a Normal Distribution shape justifying a k=2 for 95%.

If there were an easy way to create a U-Shaped Monte Carlo in Excel, I would do that, but it is basically the same issue, one rectangular in a budget by itself results in 115% containment (goofy). Plus, the ISO GUM references this same scenario, providing added insight, of which a few quotes are also included in the PDF presentation. Refer to the ISO GUM for review of the entire Annex G. Particularly Annex G.2. Annex G of the ISO GUM contains a whole lot of information regarding important aspects regarding uncertainty expansion, which has been incorporated into UncertaintyToolbox™.