I need help classifying this problem. If you know how to go about it, I'd love to hear it, but I mainly need keywords to conduct careful research.
There is a set of machines that experience failures in a very precise way: component A always fails before component B. After both are replaced, the machine will work with no issues for all time. The time between A failures and B failures fits a particular distribution.
There's an arbitrary cutoff point where one can say that failure of A didn't cause failure of B, i.e. A failed but B didn't fail any time soon afterward. The data is comprised of timestamp pairs of (a_failtime, b_failtime), where some pairs don't have a B failure (yet?).
Taking that particular set, where there are no B failures (but cutoff has not been reached), I need to estimate the number of replacement B parts I need, strictly to cover B failures that will result from these A failures.