Consider a system consisting of n independent binary components. Suppose that each component has a random weight and the system works, at time t, if the sum of the weight of all working components at time t, is above a pre-specified value k. We call such a system as random-weighted-k-out-of-n system. In this paper, we investigate the effect of the component weights and reliabilities on the system performance and show that the larger weights and reliabilities, the larger lifetime (with respect to the usual stochastic order). We also show that the best random-weighted-k-out-of-n system is obtaind when the components with the more weights have simultaneously more reliability. The reliability function and mean time to failure of a random-weighted-k-out-of-n system are stated based on the reliability function of coherent systems. Furthermore, a simulation algorithm is presented to observe the mean time to failure of random-weighted-k-out-of-n system.
