Redundancy Allocation Problem in <i>k</i>‐Out‐Of‐<i>n</i> Systems With Dependent and Heterogeneous Components

ABSTRACT The aim of this paper is to investigate the problem of one and two active redundant components allocation in a k ‐out‐of‐ n system with dependent components. Here, some necessary and sufficient conditions are presented under which the redundancies are optimally allocated to the system components based on the usual stochastic order criterion. In addition, it is shown that, unlike the independence mode, a redundant component is not necessarily allocated to the weakest component. Further, in the case of the two redundant components, the weak (strong) redundant component is not necessarily allocated to the stronger (weaker) component of the system. Some algorithms are also presented for calculating the reliability of the considered system under the assumption of dependency between the main and redundant components. Using different copula functions for describing the dependencies between components, various examples are given to illustrate the optimal allocation of redundant components.