Multi-state k-out-of-n system model and its applications

The binary k-out-of-n system is a commonly used reliability model in engineering practice. Many authors have extended the concept of binary k-out-of-n system to multi-state k-out-of-n systems, but with a limitation that k is assumed to be a constant at all the system levels. In this paper, a new definition of the multi-state k-out-of-n system is presented. Under the proposed definition, maintaining at least a certain system state level may require a different number of components to be at a certain state or above. The multi-state k-out-of-n system model has more complex properties than binary k-out-of-n systems. Increasing and decreasing multi-state k-out-of-n systems are two special types of the multi-state k-out-of-n system. The increasing multi-state k-out-of-n system has the dominant property, and as a result, we can treat it as a binary k-out-of-n system for each fixed required system state level. The decreasing multi-state k-out-of-n system does not belong to the dominant multi-state system group, and consequently, we can not extend all results from the binary k-out-of-n system to it. Examples are given to illustrate that the multi-state k-out-of-n system model can be used to describe various engineering systems.