A general formal approach for fuzzy reliability analysis in the possibility context

In this paper we focus on the fuzzy reliability analysis in the posbist reliability theory. In accordance with this theory the system failure state is defined precisely and the system failure and repair behaviour is fully characterized in the context of possibility measures. To formalize the reliability analysis in the posbist theory we propose a general approach on the basis of a system of functional equations. The solution of the system allows us to obtain fuzzy reliability characteristics of the arbitrary repairable and unrepairable systems. To illustrate the construction and application of the system of functional equations, various examples are given.