Inverse(?) of Survival Analysis

Question

I've been using the R package 'survival' recently.

I understand the way to read the survival curves is given time X what is the percent of widgets still in the field Y. And I can get a confidence interval around Y.

But I've been asked if I can go the other way around. Given a percent still in field Y, can I get a time X (and a confidence interval around X) that matches?

I'm looking for either a function in the R package 'survival', or the theory behind generating this.

Answer 1

This is called prediction of the remaining life. There are many methods to do this, parametric and semiparametric. See for instance:

Prediction of remaining life of power transformers based on left truncated and right censored lifetime data

The idea is to estimate the probability that individual $j$ will fail/die at time $t$ given that it has survived until $t_j$. This is $P(T\leq t\vert T>t_j)$, with $t>t_j$.