Failure times may be modeled as a function of explanatory variables. The Accelerated Failure Time model (AFT model) is often used for finding the relationship between failure times and explanatory variables.
In a reliability engineering context, for instance, an Accelerated Life Test is often used for determining the effect of variables (such as temperature or voltage) on the durability of some component. For relating the variables to the durability of the component, the reliability engineer usually employs an AFT model.
The following R code computes the likelihood based confidence intervals at specific values of the explanatory variables for 1) the cumulative probabilities, and 2) the quantiles. Note that a reliability engineer may refer to the cumulative probabilities as failure probabilities, and to the quantiles as life time quantiles.