Lost capacity of the weighted k-out-of-n system with discrete component lifetimes

In this paper we consider a weighted k-out-of-n system. Each component has a positive integer-valued weight assigned interpreted as its total capacity. The system is in a working state if the accumulated weights of all working components are at least k. The component lifetimes may be dependent and non-identically discretely distributed random variables. The primary focus is the capacity lost by the system upon its failure, for which we derive the probability mass function. This quantity has a potential that enables optimal system design. We also provide two numerical examples which give a demonstration of the theoretical results.