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.
How many 95% confidence bands of B failures will fall within a given time interval?
Whatever I'm missing makes me feel like that problem is magnitudes simpler, but is not the same problem.
The variance of the length of time between an A failure and a B failure is large and not normal. Does that matter?
My only lead so far is density estimation (but confidence intervals for that seem to be outside of the realm of everyday practice, whereas my question seems ubiquitous.
Last edited by nik.shornikov; 06-11-2012 at 11:38 AM.
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