Mixed Three-State K-Out Systems With Components Entering at Different Performance Levels

Abstract

In this paper, we study a three-state k-out-of-n system with n independent components (k = (k(1), k(2))). Each component can be in a perfect functioning state (state "2"), partially working (state "1"), or failed (state "0"). We assume that, at time t = 0, n(1) components are in a partially working state while the rest n(2) components are fully functioning (n = n(1) + n(2)). The system is considered to be at state "1" or above if at least k(1) components are working (fully or partially). If at least k(1) components are working and at least k(2) components are in a perfect functioning state, we shall say that the system is at state "2". In this paper, we develop formulae for the survival functions corresponding to the two different system's states described above. For illustration purposes, a numerical example which assumes that the degradation occurs according to a Markov process is presented.