Some aging properties of the residual life of k-out-of-n systems

The k-out-of-n structure is a very popular type of redundancy in fault-tolerant systems. It has been applied in industrial, and military systems. In this paper, we investigate the general residual life (GRL) of a (n-k+1)-out-of-n system with i.i.d. components, given that the total number of the failures of components is less than l - 1(1 ≤ l < k ≤ n) at time t ≥ 0. It is shown that the GRL is decreasing in I in terms of the likelihood ratio order; Behavior of IFR, and NBU of life distributions arc discussed in terms of the monotonicity of GRL. Finally, comparison of the GRL of two (n - k + 1)-out-of-n systems are conducted given that the lifetime of their components arc assumed to be ordered in the hazard rate order.