What is the advantage of doing a static test fire before launch?

Question

Continuing the series of questions (part 1, part 2) inspired by the recent loss of the AMOS-6 satellite during a static test fire, here's one thing that puzzles me a bit:

What kinds of problems is a static test fire (with the payload in place) supposed to avoid?

I would assume, perhaps naïvely, that in order for a static test fire before launch to make sense, there would have to be a reasonably large class of failure types that are:

1. detectable in a static test fire,
2. not reliably detectable without the test fire,
3. serious enough to threaten mission success if only detected after launch, and
4. unlikely to result in "rapid unscheduled disassembly" and total loss of the vehicle and payload if they occur during the test fire.

Given that e.g. SpaceX does run a static test fire before launch, and that they're not stupid, I assume that there must be enough of these kinds of problems for the test fire to make sense. But as a layperson with only a casual interest in rocketry, I'm having a hard time figuring out what they are. Or perhaps there are some other reasons for the test fire?

Obviously, if the test fire was conducted without the payload, I could see it making sense; in the event of catastrophic failure during the test fire, you'd only lose the really expensive launcher, but not the also really expensive payload. But with the payload in place, RUD during the test fire is hardly a better outcome than RUD during launch. I would also expect there to be at least some "bad luck" failure modes that occur only rarely, and are difficult to detect before they do occur (meaning that a test fire before launch effectively just doubles the risk of those failure modes). Given that a test fire isn't free, either, surely there must be some major advantages to it that outweigh these costs and risks.

Answer 1

Test fires have many purposes. The engines themselves were individually fired at the McGregor, TX facility, then shipped back to Hawthorne, CA to be mated to a stage. That entire stage was shipped to McGregor, TX and test fired as a stage.

Then it was shipped to CCAFS, Florida or Vandenburg to be launched.

Product may settle in shipping?

Things can happen. One more test on the pad, ensures everything is go for launch. I read somewhere that Jonathan Mcdowell of Jonathons Space Report fame looked it up and the last RUD during a test fire was in the 1960's. So this is not a common outcome.

But the static fire does test that the engines are all good to go after travelling across the country the slow way.

But it also tests the Ground Support Equipment (GSE) which seems like the likely culprit at the moment (that could change) and we saw during the first several F9 Full Thrust launch campaigns that the GSE was a problem.