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

A k -out-of- n system with weighted components is a system that consists of components contribute differently to the overall performance of the system, and functions if the total weight/contribution of all working components exceeds or equal to the level k . Such a system is useful and suitable for modeling capacity based systems such as power systems, transportation systems and manufacturing systems. This paper is concerned with the lost capacity by the weighted- k -out-of- n system at the time when the system fails. This random quantity is useful for making an optimal decision about the spare capacity that should be available to renew the system upon its failure. In particular, the distribution of this random quantity is derived and the theoretical results are illustrated for a power system consisting of a specified number of generating units.