I. Introduction
Multi-State System (MSS) modeling has been widely applied to resolve system availability and reliability assessment problems [1], [2]. Under this framework, the performance of each component is discretized into more than two exclusive states from perfectly functioning to complete failure, and each state is characterized by a probability of occurrence. In general, the intermediate state can be decided through the level of degradation of the component or system function requirements or both. Many components are subject to natural deteriorations which can render them partially functioning, and the system function requirement might force one component to reduce its performance level, even if it bears no degradation. Compared to binary-state system (BSS) models, the MSS models offer higher flexibility in the description of the system state distribution and evolution, for more precise approximations of real-world systems. MSS is a modeling framework capable of handling both availability and reliability assessments. In this paper, we focus on availability assessment assuming the system is repairable.