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We are interested here in some failure times due to wear or aging. The main aim is to jointly model the degradation process and one (or more) associated failure time(s). Two main joint models exist. The first one considers a failure time which is directly defined by the degradation process (degradation failure) as a hitting time of growth curve with random coefficients; the second one considers that the degradation influences the hazard rate of a failure time by a conditional definition of its survival function (traumatic failure). When both modes of failure exist, only the first one is observed. Very often, longitudinal observations of degradation values (measured with error) are available for each item until the first failure. We are mainly interested here in the nonparametric estimation of the cumulative intensity function of the traumatic failure time and related reliability characteristics. [ABSTRACT FROM AUTHOR]