Dynamic Fuzzy Reliability Analysis of Multistate Systems Based on Universal Generating Function

Considering the fuzziness of load, strength, operational states, and state probability, reliability models of multistate systems are developed based on universal generating function (UGF). The fuzzy UGF of load and the fuzzy UGF of strength are proposed in this paper, which are used to derive the fuzzy component UGF and the fuzzy system UGF. By defining the decomposition operator and the inner product operator, failure dependence and effects of multiple load applications are taken into account in the established reliability models. Moreover, dynamic fuzzy reliability models of multistate systems are constructed considering the strength degradation of components. The results show that failure dependence and the effects of multiple load applications have significant impacts on system reliability, which considerably decrease system reliability and increase the fuzziness of system reliability under low performance requirements. Besides, in the dynamic reliability analysis of multistate systems, strength degradation dependence could lead to large computational error.