RELIABILITY OF A MULTI-STATE CONSECUTIVE k-OUT-OF-n: G SYSTEM

Fortunately traditional reliability theory, where the system and the components are always described simply as functioning or failed, is on the way to being replaced by a theory for multistate systems of multistate components. In this paper, we treat the consecutive k-out-of-n systems. Such systems have caught the attention of many engineers and researchers because of their wide range of application. We define a multistate consecutive k-out-of-n system: G as follows: Each component and the system can be in 1 of M + 1 possible states: 0, 1, 2, …, M. The system is in state ≥ j iff at least kj consecutive components are in state ≥ j. The value of kj can be different for different required minimum system state levels. We propose a method based on the combinatorial approach for computing the system's reliability and we give examples to illustrate this method.