One thing I keep meaning to ask that I've been curious about since watching one of the James Burke episodes were he mentioned the 99.99992% reliability standard every component was built to for the Apollo missions. What kind of standard is set for commercial satellites and NASA unmanned missions? There must be some kind of sliding scale depending on how expensive the mission or satellite is but were would it start at? 95% for a relatively cheap satellite for example? I imagine that reliability figure must make a difference with the insurance premiums as well.
That's a hornet's nest of a question because system reliability and component reliability are different things. You build components to a certain number of "nines" of reliability because the way they combine into a system invokes statistical computations to determine the statistical reliability of assemblies, subsystems, and entire systems for the span of a given mission. I mentioned I worked (in the early phase) on the Antares rocket, which was originally in a class of rockets generally considered to have only 1-2 "nines" overall. A 1 in 20 failure rate is acceptable for some applications, especially when a goal is to reduce cost per launch. But in order to get even that amount, several of the components have to be built to 3-4 "nines" (i.e., probability of success during a mission > 0.9995).
Here's a simple example. Let's say your car has four tires and each tire is built to two nines, or probability of "mission" success for each tire is 0.99. But all four tires have to work, so you multiply them together to get the overall reliability for the tire "subsystem" -- algebraically,
psys =
pcnc where
c denotes a component. You end up with 0.96. By needing four of the components in order for the system to work, you lose almost half a "nine" in the tires' contribution to overall trip success.
Conversely you can design things so that component reliability works in your favor. If you really need a rocket engine to fire, you can have two parallel (i.e., redundant) fuel paths, each with its own inlet valve. The idea is that only one of them has to operate in order for the engine to fire. If you want 4 nines for that engine then the combinatorial math works the other direction. It means you can tolerate a
p <= 0.0001 probability of failure, which means that's the probability of
both inlet valves failing. That involves the
nth root,
n = 2, and thus acceptable component failure is
p <= 0.01. You only need two nines of reliability on the valves by arranging them redundantly.
Doing this for an entire design, using appropriately sophisticated statistical methods, complexity analysis, and criticality analysis, you come up with reliability budgets at different scopes of examination in the design. And unfortunately for component-level designers, this often means that critical components need to be built to unbelievably high reliability factors.
