Comparisons of kk-out-of-nn systems with heterogenous components

The kk-out-of-nn structure is a very popular type of redundancy in fault-tolerant systems which has been widely applied in reliability engineering and system security. In this paper, we carry out stochastic comparisons between kk-out-of-nn systems with independent heterogeneous components with respect to various stochastic orders such as hazard rate order, mean residual life order, and reversed hazard rate order. Moreover, we also establish likelihood ratio ordering results of series and parallel systems in multiple-outlier models.