A generalization of the weakest link distribution family (WLDF) developed in [1, 2] and its application to the carbon fiber material strength data processing are presented in this paper. As in [1, 2] we consider the specimen as a chain of n elements (links). The fracture process is modeled as follows: in the first stage initiation of defects (before loading or during loading) and in the second stage a specimen fracture take place. As distinct from our previous publications, the strength of items without defects is taken into account; two types of defects (independent on load (“technological”) and dependent on load) and corresponding two types of the influence of defect number on the specimen strength are considered. It is shown that for carbon fiber material some models from WLDF and linear law (LW) traditional Weibull model provide some better prediction of strength-length dependence than power law Weibull regression model which sometimes provides better fitting of experimental data.