Convex Sublattice Based Reliability Theory

Classical probability theory has been widely used in reliability analysis; however, it is hard to handle when the system is lack of adequate and sufficient data. Nowadays, alternative approaches such as possibility theory and fuzzy set theory have also been proposed to analyze vagueness and epistemic uncertainty regarding reliability aspects of complex and large systems. The model presented in this paper is based upon possibility theory and multistate assumption. Convex sublattice is addressed on congruence relation regarding the complete lattice of structure functions. The relations between the equivalence classes on the congruence relation and the set of all structure functions are established. Furthermore, important reliability bounds can be derived under the notion of convex sublattice. Finally, a numerical example is given to illustrate the results.