I have noticed on different occasions that the shield value for any particular unit is not always the same with each simulation. Given that any unit has a base shield value, and that each tech upgrade increases that value by a set rate, shouldn't the shield value during any simulation be constant? Or is there a reason that it is not?

Weapons and shields both have a factor of randomness in sims. As your techs increase the values do get better overall, but they also have a wider range of possible values. This is some stuff I got from a few tests I ran a long time ago (so with the old engine):

Lvl 10 WSA

Upper/Lower Limits
Weapons/Shields: (base +- (base * 0.2)) * 2
Armor: structure/5

Range: (base * 0.2) * 4
Increment: Range / 40

The "base" is the value of the ship's stats (either weapon or shield). Obviously this will change with different techs, but I never got to the point of testing for different levels of WSA. And it's also possible this is way off, but that's what I got from my tests, so feel free to confirm or disprove it.

Well, to be honest your response got me curious, so I ran some tests of my own using the current simulator. I used small cargoes in the tests because the base shield value (10) and weapon value (5) is easy to work with. I came up with the following, where "base" is equal to the value given in the stats, and "tech" is equal to the levels of WSA:

Armor -
base = structure / 10
base + ( base * 0.1 * tech)

Upper / lower limits for shield & weapon -
adjusted base (adj) = base + (base * 0.1 * tech)
[adj +- (adj * 0.2)]
Note: these values are displayed with rounded values in the simulation

Range = adj * 0.4

I also found this to hold true for other ships. There is still some randomness in which value out of the range is actually used in any given simulation, but this at least gives worst and best case values for any particular unit with a certain level of WSA.