Software faults are not included in reliability calculations because a software fault is a design issue. Developing SW in accordance with DO-178C (or predecessors) is intended to ensure that these faults are minimized. The reasoning that it's not measured as reliability is that when there is a SW fault it's not a broken box on the plane that has to be fixed, that fault is a potential failure on every aircraft that has the same system.
Swapping out a unit for a SW fault doesn't solve the problem. It's going to take a service bulletin (SB) with new SW deployed to the fleet to fix it.
So reliability is about hardware failures. Basically, parts break. Some break more often than others. The more parts you have, the more likely something will break. So making things more reliable is about minimizing parts and using the most reliable parts you can. But there are limits to what you can do. A power transistor will be less reliable than a resistor, but if you need it, you have to have it. But having one or two instead of 3 or 4 will improve reliability. I suggest a read of MIL-HDBK-217 which is the industry standard for predicting reliability.
So an IMA improves reliability by reducing the number of Line Replaceable Units (LRUs). Fewer LRUs means fewer cables, connectors, power supplies, and processors. An IMA can run multiple functions on a single processor card instead of having a dedicated unit for each function. All that means fewer parts to fail and higher reliability.
Aside from parts count, the biggest drivers of electronics failures are heat (high temps and high temperature swings) and vibration. Which is why some manufacturers perform Highly Accelerated Life Test (HALT) to identify weak points in the design early.
Nothing will solve the issue of parts obsolescence. Parts will go obsolete. It's a huge problem in aviation where products hang around for 20 or more years. An IMA does help manage the obsolescence issue. It does it by having a bunch of common processor boards. Not only do IMAs have fewer total parts, they have fewer unique parts which mean fewer parts that can go obsolete. Fewer parts going obsolete will mean less work to replace them.
It's still a complicated process to deal with, but if a part becomes non-procurable on an IMA processor board you'll need to modify the board design to use a new part. That can be a fairly straight-forward part replacement (equivalent part) to a major redesign of the circuit board. In the end, the new board has to be equivalent to the old one. That way it can be swapped out without impacting anything else (software or hardware).