I have a failure rate problem involving structural beams. The scenario is that a set of $n$ structural beams are supporting a weight of $W$ kilograms. For the purpose of simplification, we can assume that all the structural beams equally support the weight. And so, we can say that, if $l$ of the beams break, then the load will then be equally shared by the remaining $n - l$ beams. When we reach the point where $n - 1$ of the beams have broken, new beams are instantly installed to increase the number of working beams back to $n$.
This is an instantaneous failure rate problem. In this case, the rate of failure of any single beam carrying $W^\ast$ kilograms is $\alpha W^\ast$, where $\alpha > 0$ remains constant. Furthermore, this is a Markov process, meaning that the time until failure at time $t$ is independent of the past.
So it seems to me that we can model this problem as a Markov process with $X(t)$ being the number of unbroken beams at time $t$. Furthermore, it seems to me that we have $1 \le l \le n - 1$.
Let's say we're given some failure rate for the structural beams, measured per year per kilogram of weight supported. How do I calculate the probability that some system will survive for some years before replacement beams have to be installed? I'm not so much interested in specific numbers as I am the concept (so that I can make it work for any values I want, based on the specific problem), so feel free to input your own numbers for purposes of illustration.