Mixture Representations for Three-State Systems With Three-State Components

This paper is concerned with dynamic reliability modeling of three-state systems consisting of three-state s-independent components. The components and the systems are assumed to be in three states: perfect functioning, partial performance, and complete failure. Survival functions of such systems are studied in different state subsets. It is shown that the survival function of a three-state system with a general structure can be represented as a mixture of the survival functions of the three-state k-out-of- n:G systems. The results are illustrated for the three-state consecutive- k-out-of- n:G systems whose components degrade according to a Markov process.