I have the following problem.
I want to estimate the pdf of the life time of a component.
I have data from all components that have failed before time t1.
I also know the fraction of components that have failed before time t1.
So: I know for each component that failed before time t1 how many days d it was used before failure (d<t1), and I know that out of n components m failed before the warranty time had elapsed (m/n ~ 10%).
How can I use this information to estimate the probability of failure as a function of time?
We can assume that the function will only have one peak.