Stochastic Comparisons for k-out-of-N(F) System of Random Numbers of Units

In this paper, stochastic comparisons for -out-of- ( ) system with random numbers of identical components are studied. The lifetime of -out-of- ( ) system corresponds to the kth order statistic of random numbers of independent identically distributed random variables. Character- izations based on some stochastic orders, for example, star order, hazard rate order and reversed hazard order system are studied. Stochastic order has been widely applied in computer queuing networks, communications systems, automated production line system, inventory systems.