The Reliability of Weighted k-out-of-n Systems with Randomized Components of Several Batches
One of the most important types of redundancy structures is weighted k-out-of-n system (which briefly denoted as weighted k/n system). In this paper, a weighted k/n system with dependent components is considered and it is assumed that the components of the system are selected from p, p≥3, batches. The components in the batches are different in terms of their weights and reliability functions. It is supposed that the selection of components from p-1 batches is based on a random vector with dimension p-1, and the remaining components are chosen from the last batch. The structure of dependency of components is also determined using a copula function. Under these circumstances, a mixture representation is given for the reliability function of the system based on the reliability functions of weighted k/n systems with a fixed number of the components in the batches. Some stochastic orderings are presented, under some conditions, for comparing two different weighted k/n systems with randomized components. The results are illustrated using some examples and graphs.