Suppose that we monitor a population of devices over an interval $[a,b]$. Some devices are added before $a$ and some are added during $[a,b]$. Furthermore, some devices fail during $[a,b]$ and some are healthy until time $b$ and their ages are right censored. Roughly, $90\%$ of the population are right censored. We can assume that the devices are added randomly. We know all device ages during $[a,b]$.
Is this an example of a random censoring? I'm using the following type definitions from Wikipedia: https://en.wikipedia.org/wiki/Censoring_(statistics)#Types
We are interested to perform survival analysis to estimate the failure distribution $f(t)$ of these devices. My intuition is that since many of the samples are right censored, our estimation of the tail of distribution $f(t)$ will be inaccurate and biased.
Now, suppose that we are only interested in estimating $f(t)$ over the interval $[0,c]$ where $c < b - a$. Is there a way to obtain an unbiased estimate of $f(t)$ over this interval? Also, we have a lot of data so it is okay to only use a fraction of them.