# Provision Spares at Confidence Level

We sell systems comprising line-replaceable units (LRUs). We know how many operating hours have accumulated on each LRU type (because we know when they went into service, and we ask our customers what their operating tempo is), and we know how many failures have occurred by LRU type (because they send them to us for repair).

I can calculate the MTBF confidence interval for each LRU (using NIST's formula for a Constant Repair Rate Model) at a given confidence level, and I know how to use inverse Poisson to calculate the max failures at some confidence if I knew the actual MTBF.

My question is, given operating hours and failures by LRU, and the number of LRU operating hours required for the remaining lifecycle, how do I calculate at some specified confidence the number of lifetime spares a customer should buy when they come into diminishing supply? I'd have thought this would be pretty common calculation.

So I'm looking for a function like this: