I have number of water tanks, I want to calculate the probability that a water tank of age $a=i$ is leaking, $L(a=i)$
I calculate the conditional probability $l(a)$, of a water tank leaking given that it hasn't leaked previously as a function of age and then compute
$L(i) = l(i-1) + [1-l(i-1)]\times l(i)$,
The probability a tank is leaking at age $i$
I posted a recent question on how best to calculate $l(a)$ and I was pointed in the direction of survival analysis. I've computed the Survival function and the Hazard but I have now confused myself as to how these relate to the above.
If the survival function in the context of this question gives the probability that a leak has not yet occured at age $i$, $S(i) = P(a>i)$, then is
$L(i)=1-S(i)$, the probability that a leak has occured at $a\leq i$?
If the Hazard function, $h(i)$, in this context gives, for a tank that has not leaked at age $i$, the probability that it will not leak until age $i+di$, then is
$h(i) = l(i)$?
and if my understanding is incorrect, then how do I relate survival analysis to my problem in order to calculate $L(i)$, the probability that a tank is leaking at age $i$