Stochastic comparisons on total capacity of weighted k-out-of-n systems with heterogeneous components

This paper carries out stochastic comparisons on the total capacity of weighted k-out-of-n systems with heterogeneous components. The expectation order, the increasing convex/concave order and the usual stochastic order are employed to investigate stochastic behaviours of system capacity. Sufficient conditions are established in terms of majorisation-type orders between the vectors of component lifetime distribution parameters and the vectors of weights. Some examples are also provided as illustrations.