Preservation properties of some relative aging classes under $(n-k+1)$-out-of- $n$ systems

In this paper, we focus on two relative aging classes, namely increasing (decreasing) relative failure rate and increasing (decreasing) failure rate relative to average failure rate. We studied some reliability properties and connections with other classes of lifetime distributions. The main objective of this paper was to investigate the preservation properties of decreasing relative failure rate class and decreasing failure rate relative to average failure rate class under the structure of ( $n-k+1$)-out-of- $n$ system. We give some examples of parametric distributions to evaluate the correctness of the results.