Uncertain<T>

for mechanical engineering drawings to communicate with machinists and the like, we use tolerances

eg. 10cm +8mm/-3mm

for what the acceptable range is, both bigger and smaller.

id expect something like "are we there yet" referencing GPS should understand the direction of the error and what directions of uncertainty are better or worse

Something that's bugged me about this notation though is that sometimes it means "cannot exceed the bounds" and sometimes it means "only exceeds the bounds 10% of the time"

I don’t think I’ve ever seen mechanical drawings have “90% confidence” dimensions like this. If a part’s too big then it won’t fit, and it’s probably useless.

If a test procedure is verifying all dimensional accuracy, it can be assumed to be bounding tolerance. If it's a mass production line with less than 100% testing of parts, you'd have to expect that some outliers get by and the tolerance is something like 3-sigma on a Gaussian.

Or for something likely relevant to many here - 3 point time estimates for project planning.

Probability distributions (even very simple ones) provide a much clearer view across any domain where there’s inherent uncertainty.

Yeah it's probably field specific and I guess Gaussian-based uncertainty would be more about statistical sampling rather than tolerances. I've noticed that if arithmetic is being done on it it's almost certainly Gaussian. I just mean whenever I see uncertainty like this, I don't know what is meant!

In Mechanical Engineering, tolerances ensure that when you put parts together, they will fit as long as the tolerances were respected.

It's not statistical. If the machinist makes a part that's not within the +/- bounds, they throw it away and start again. If you tried to fit multiple parts, all with only statistical respect for tolerances, you would run into trouble almost 100% of the time with just a few pieces.

Yeah understood. In electronics: Resistor values are Gaussian but they test and bucket the resistors so that they can be treated as tolerances for similar reasons.