A Universal Generating Function in the Analysis of Multi-state Systems

Abstract

Almost all work in reliability theory is based on the traditional binary concept of reliability models allowing only two possible states for a system and its components, viz, perfect functionality or complete failure. However, 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 (MSS). For MSS, the outage effect will be essentially different for units with different performance rates. Therefore, the reliability analysis of MSS is much more complex when compared with binary-state systems. The recently emerged universal generating function (UGF) technique allows one to find the entire MSS performance distribution based on the performance distributions of its elements by using algebraic procedures. This chapter presents the generalized reliability block diagram method based on UGF and its combination with random processes methodology for evaluating the reliability of different types of MSS.