Estimation of total time on test transforms for stationary observations

By proving Chibisov-OʹReilly-type theorems for uniform empirical and quantile processes based on stationary observations, we establish a nonparametric large sample estimation theory for total time on test transforms. In particular, we obtain weak approximations for total time on test transforms also under the assumption of positively associated dependence, a kind of dependence that is encountered in many practical life testing situations. We derive similar asymptotic results for mixing sequences as well, another and often used structure of dependence for sequences.