Ok here is the math stuff.
I tried several types of equation to find the most satisfying form and settled for the one shown below. For the sake of simplicity, all equations will be presented focusing on the shield capacity, but the structure is the same for other stats.
Capacity = Base_capacity * (1 + Body_cap_coeff + Capacitor_cap_coeff + Battery_cap_coeff)
Body, capacitor and battery coefficients depend on the manufacturer. The higher the better, except for recharge delay for obvious reasons. Because body, capacitor and battery modify shield stats equally, we have, for a given manufacturer and a given stat, the following property:
Body_cap_coeff = Capacitor_cap_coeff = Battery_cap_coeff = Manufacturer_cap_coeff
For example, in the case of a pure tediore shield, the capacity equation is
Capacity = Base_capacity * (1 + 3 * Tediore_cap_coeff)
For one bandit part and two hyperion parts it is
Capacity = Base_capacity * (1 + Bandit_cap_coeff + 2 * Hyperion_cap_coeff)
In order to avoid negative coefficients, base stats will always be the lowest stats possible which a pure manufacturer, with the one providing the smaller contribution to the stat. For example, the base capacity will always be the capacity of a pure Maliwan shield, every other part combination resulting in higher capacities.
Note that the base stat choice is subjective, and in my opinion taking the lowest stat value possible results in easier to understand numbers. Depending on the manufacturer and the stat considered, coefficients will vary in the range [0 ; 1], though I will also display them as percents of the base.
The table below shows which manufacturers are used as base for each stat. There are also base values associated to purple adaptive shields at level 70 but keep in my mind those values are only compatible with this type of shield, whereas manufacturers coefficients are valid for ANY shield in the game.

Now let’s see manufacturers’ contributions. This table displays coefficients you should use for calculation,

And those values in percents for easier reading

A few graphic to better visualize differences between manufacturer parts on shield stats,
Feel free to ask any question,
@Hoyle4 Thanks for providing the data it really helped