Investigation of structural reliability of P-networks with independent and dependent elements failures

Any monotone P-network (indecomposable-parallel structure) is formed by the superposition of the simplest indecomposable networks, which are the “building blocks” of indecomposable-parallel monotone structures. Polynomials of structural failure (reliability), calculated using the logical-probabilistic and fuzzy-possibilistic approaches, derived from the assumption of independence of elements failures. The analysis of structural reliability of the simplest indecomposable networks for the case of dependence of elements failure by condition of homogeneous and heterogeneous structure is carried out. It is conjectured that the obtained relations between the integral possibilistic and probabilistic estimations of homogeneous and heterogeneous networks will be kept for any P-networks. The results of the study of integral indicators of structural reliability for the P-networks composed of six elements are given.
It can reveal the following patterns for the indecomposable-parallel structures:
– obtained integral estimates of a failure of homogeneous and heterogeneous networks in terms of independence of failures of structures elements are the upper and lower boundaries of the integral index of structural reliability (failure) of the system;
– integrated probabilistic assessment of a homogeneous structure situated between the integrated probabilistic assessment of heterogeneous networks and index of the possibility of structural reliability (failure);
– when approaching considered P-networks to their limit state (the most reliable and most unreliable P-networks) values divergence of integral parameters is observed that allows us to introduce scale of structures comparison, reflecting the presence in the structure of duplicate links.