The Usefulness of Complete Lattices in Reliability Theory

Abstract

The main aim of this paper is to show how lattice theory in the very next future will be a useful tool in analysing complex real reliability problems, not properly modelled within classical reliability theory. The introduction of a complete lattice as a state space appears not only of theoretical importance that allows to understand several phenomena with respect to reliability theory better, but as a need claimed from practical engineering. Two important topics are discussed in this general framework: incomparability of component and system states and the duality principle. The strong relationship between the ideas of fuzzy set theory and the ideas that led to the introduction of the theory of multistate structure functions will become clear.