Reliability evaluation of circular k-out-of-n: G balanced systems through minimal path sets

This paper studies a circular k-out-of-n: G balanced systems with identical and independent spatially distributed units. The system consists of an even number of units n which have constant survival probability r and failure probability 1 - r. The system is operating if at least k units are operating and it is balanced. A new balance definition is proposed for this system and the system reliability is calculated when the existing and the proposed system balance conditions are considered. The minimal path sets of the system are considered in the evaluation of the system reliability. The difference between the system reliability values reinforces the need to carefully select the system balance definition, depending on the system.