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Most books on reliability theory are devoted to traditional binary reliability models allowing only two possible states for a system and its components: perfect functionality and complete failure. Many real-world systems are composed of multi-state components, which have different performance levels and several failure modes with various effects on the system’s entire performance. Such systems are called multi-state systems (MSSs). Examples of MSSs are power systems or computer systems where the component performance is respectively characterized by the generating capacity or the data processing speed. For MSSs, the outage effect will be essentially different for units with different performance rates. Therefore, the reliability analysis of MSSs is much more complex when compared with binary-state systems. In real-world problems of MSS reliability analysis, the great number of system states that need to be …