Two plural nouns in a row

I would use the singular for the first word in most of your examples:

• "component reliabilities"
• "component failures"
• "word combinations"

but

• "systems designers" This is different because the singular form is (or can be) a "systems designer" -- as a job title of someone who designs many systems, for example. "System designer" may be more appropriate if you're talking about a specific system: "This machine is useless. The system designer must have been an idiot".

You're forming a compound noun from 2 nouns, just not a familar one like "bus stop"

Changing the structure can make things better, it's not exactly a matter of word order though: "Component failures tend to release the magic smoke" is good, but "Components' failures tend to annoy their owners" also works. This last example uses the possesive plural (equivalent to "failures of components") and isn't a compound noun.