On the stochastic and dependence properties of the three-state systems

Abstract

Suppose that a system has three states up, partial performance and down. We assume that for a random time T1 the system is in state up, then it moves to state partial performance for time T2 and then the system fails and goes to state down. We also denote the lifetime of the system by T, which is clearly T = T1+T2. In this paper, several stochastic comparisons are made between T, T1 and T2 and their reliability properties are also investigated. We prove, among other results, that different concepts of dependence between the elements of the signatures (which are structural properties of the system) are preserved by the lifetimes of the states of the system (which are aging properties of the system). Various illustrative examples are provided. © 2014, Springer-Verlag Berlin Heidelberg.