Reliability analysis of weighted-k-out-of-n system consisting of three-state components

The reliability of a weighted-k-out-of-n system that consists of three-state components is studied. The system is assumed to comprise n three-state components, namely, perfect functioning, partial working, and complete failure and functions if the total weight of all the working components is at least k. Reliability expressions are presented when the times spent by components in perfect functioning and partial working states are dependent with a given joint distribution. Sufficient conditions are also provided to compare the expected total weights of two systems.