The lost capacity by the random weighted-k-out-of-n system

A k-out-of-n system with random weights for components is a n components re- liability system with the performance level of at least c, which it operates if the total weight of all working components is at least c with the total working components of at least k. Queueing systems can be considered as a suitable real example of the random weighted-k-out-of-n system. The lost capacity by the system is useful to decide how much spare capacity should be accessible to renew the system upon its failure. This paper investigates the lost capacity by the weighted-k-out-of-n system with random weights at the time when the system fails.