Modeling the interdependency between natural degradation process and random shocks

In this paper, an interdependent structure between the natural degradation process and random shock process is proposed and incorporated into the competing failure model. Interdependent means that shocks are assumed to have an impact on the natural degradation process, additionally, the natural degradation process can also influence random shocks. Therefore, the interdependent structure includes two-fold: a) the impact of random shocks on the natural degradation process, represented by the cumulative damage adding up to the natural degradation process and expressed by a compound Poisson distribution, which is commonly used by other researchers; b) the influence of natural degradation process toward random shocks (both the magnitude and damage of shocks), reflected by the natural-degradation-state varying thresholds used for categorizing shocks into safety zone, damage zone and fatal zone according to their magnitudes, and the natural-degradation-state varying cumulative damage of shocks in damage zone, which are considered for the first time. A closed-form reliability function is derived under the linear natural-degradation-state varying thresholds. Two illustrative examples are presented to demonstrate this approach, and results show that the developed interdependent relationship model can obtain a more practical estimation of the reliability.