Luckily, that's easy: the "fault model", all the ways things can break. That tends to be a lot more complex than the operating model, the domain model, or the business model.
Once all the potential issues and associated costs for all the fault models are enumerated, then QA can happily offer to any other organization the responsibility for each one, and see who steps up to take it on.
In many cases, it can be done more cheaply in design, engineering, or automation; it's usually easier to prevent a problem than capture, triage, debug, fix, and re-deploy.
Organizations commonly make the mistake of being oblivious to the fault models and failing to allocate responsibility. That's possible because most failures are rare, and the link from consequences back to cause is often unclear. The responsibility allocation devolves to blame, and blame to "who touched this last"? But catastrophic feedback is a terrible way to learn, and chronic irritants are among the best ways to lose customers and staff.