THIS PAPER CONSIDERS A GENERAL DEGRADATION PATH MODEL AND FAILURE TIME DATA WITH TRAUMATIC FAILURE MODE. IT PROVIDES A REVIEW OF THE NONPARAMETRIC ESTIMATOR OF Survival function, STUDIED BY BAGDONAVICIUS, AND CONSIDERS THE PARAMETRIC ESTIMATION OF Survival function OF FAILURE TIMES WITH A HAZARD RATE IN THE DEGRADATION SPACE. IN ADDITION, WE DISCUSS THE COMPARISON OF BOTH PARAMETRIC AND NONPARAMETRIC METHODS ACCORDING TO SIMULATED AND REAL DATA.