Preventive replacement policies of parallel/series systems with dependent components under deviation costs

In traditional reliability analysis, an important assumption is that the failure components are independent from one another. However, this assumption is often challenged in reliability engineering as practical failure process is always dependent on one another component. This manuscript bases on the method of copula to characterize the dependence of the components lifetime, and studies the preventive replacement policies of series/parallel systems with dependent heterogeneous components under deviation costs. Firstly, we provide the optimal replacement time of the series and parallel systems from dependent components in the age replacement policies under the deviation cost. Secondly, we give the optimal number of periods for series/parallel systems with dependent components to minimize the expected cost rate under deviation costs. The effects of dependency, deviation costs, and the number of components in the system on the maintenance policies are analyzed. The numerical examples are then implemented to develop the optimal preventive replacement policies that minimize the expected cost rate. A case study of the cables in high-voltage transmission networks system from dependent components is conducted to present the optimal replacement time and number of periods.