MinMaxDM distribution family for a series of parallel systems with defects and the tensile strength of a composite material

This paper is a review of the authors' previous work devoted to the analysis of tensile strength of unidirectionally fiber-reinforced composite material, considered as a series of parallel systems with defects. Additionally, a specific model is studied based on an assumption that only failure of the damaged parts of a specimen can take place. A version of the Poisson distribution is used for probability mass function of the number of defects. The proposed models allow estimating the probability of the presence of defects in order to clarify improvements of the production technology needed to increase reliability, and to predict the scale effect of tensile strength of the composite. Strength test data of different composite materials are processed and the results analyzed. A numerical comparison of different models is provided.