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A study of complete lattice in multi-state coherent system reliability analysis

Systematic reliability analysis of a multi-state coherent system (MCS) is presented in this paper. Most available models for reliability purpose are addressed under the following assumptions: (1). the state sets of the system and its components are totally ordered. (2). the system and its components are considered to be in one of two states: perfect functioning or complete failure. However, both of the two model assumptions over-simplify the reality and limit the model application. In this paper, the multi-state coherent system is analyzed on the assumption that the state sets of the system and its components are complete lattices from probabilistic and possibilistic point of view.