Reliability modeling of weighted-k-out-of-n: G system under multiple failure modes with dependent components

In engineering practice, some weighted-k-out-of-n: G systems often show multiple performance levels, resulting in multi-failure-mode mechanism. For these complex degradation systems, a novel reliability model with heterogeneous components is proposed on account of the number of working components, the total weight, and the sojourn time in some a stage, where different weights and thresholds are taken into account in different stages, and so do failure modes. After presenting the indispensable definitions of first passage time and the system lifetime, the system reliability indexes are derived by the Copula method to depict the dependence between components. Furthermore, maximum likelihood estimation of the Copula parameters is adopted and a Copula-based expression for component importance in each type is obtained. Finally, the reliability of the overall supercharging subsystem of an advanced fighter air energy system, as an example of weighted-k-out-of-n: G system with multi-failure modes is analyzed by the suggested model, which offers the comparison of independent and dependent cases. Meanwhile, sensitivity analysis is available to point out the effects on the system.