A generalized Weibull model is presented for reliability characterization of single carbon fibres. This generalized distribution gives the probability of tensile failure of fibres as a function of length, surface area and volume of fibres, separately in different models using a statistically significant experimental data set. This model accounts for the unusual variation in the strength of the fibres as the physical parameters capture the severity of the most severe flaws in the ensemble of fibres. The experimental campaign involved analysing the diametric variation in each carbon fibre using photomicrographs. The micro-texture and morphology were further analysed using scanning electron microscopy images. An extensive characterization of the strength dependence on the fibre gage length was performed through “single-fibre uniaxial tensile tests” on several hundred carbon fibres of different grades. The goal of the study is to ensure the reliability of strength characterization of a single fibre, accounting for geometric irregularities and property variation. The present Weibull models are compared to assess their descriptive accuracy, that is, the “goodness-of-fit” in describing the observed statistical data as well their generalizability in predicting future values. The Kolmogorov–Smirnov (KS) test was used to ascertain the goodness of fit for the predicted Weibull plots. It was found that the descriptive adequacy of the models improved with the increase in the number of parameters used in the definition of the Weibull model. The conventional model failed the KS test for the most number of cases and hence was deemed unfit in terms of generalizability. Furthermore, the generalized Weibull model was found to have better descriptive accuracy and predictive power compared to the conventional model. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.