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The copula function offers new opportunities for advanced engineering design and can model correlated structures between random variables in reliability; in other words the dependence can describe time varying and nonlinear features of statistical links of marginal distributions. The paper proposes the study of reliability block diagrams by the analysis of the bridge model with links like serial-parallel, parallel-serial, based on total probability formula. The proposed reliability model built by copula functions is a new possible variant for statistical approach in the quality practice.