Copula-Based Reliability for Weighted-k-Out-of-n Systems Having Randomly Chosen Components of inline-formula

摘要

In this article, we consider a weighted-$k$-out-of-$n$ system having $m geq 2$ type of components each with its own positive integer-valued weight, in which the random lifetimes of components are dependent. This system is supposed to work with performance level $k$ if and only if the total weight of functioning components of all types is at least $k$. The structure of dependence of the system component lifetimes is modeled by the copula function. Also, it is assumed that the random numbers $N_i$ of components are chosen from class $D_i$ for type $i$. The reliability of the system is obtained as a mixture of the reliability of weighted-$k$-out-of-$n$ systems consisting of $m$ types of components with fixed number of them in terms of the probability mass function of the random vector $(N_1, ldots,N_{m-1})$. Then, a copula-based expression for component importance in each class is obtained, and illustrative examples are presented.