Reliability analysis for parallel systems with different component shock sets

Reliability for parallel systems has been studied based on multiple failure processes for each component. The previous research was based on the assumption that when a shock arrives, it affects all components. However, for some applications, it is more realistic and practical to classify those shocks into different sets based on their sizes and function. That is, shocks with specific sizes or function can only affect one or more components in the system but not necessarily all components. The classification of shocks is reasonable for some applications. For example, sounds received by human's ear can be considered as shocks coming to the system. Only sounds with decibel range of 20 Hz to 20 kHz can be detected by human hearing system, which means only shocks with specific size can affect systems. The other example can be laptop. Pressing the keyboard of a laptop can also be considered as shocks to the system. Probably, it has no effect on battery reliability, which means this type of shocks has little effect on laptop's component battery. In this paper, reliability of parallel systems is studied based on multiple competing dependent failure process. Not all shocks accelerate degradation and this problem is formulated for the parallel system by the conditioning on shock sets. For each component in the parallel system, typical failure processes can be: 1) soft failure process, where the component fails when the total degradation is beyond the degradation threshold level; and 2) hard failure process, where component fails when the damage from one shock is beyond the hard failure threshold level. These two failure process are dependent since each shock has effect on both of these two failure processes. They are also competing, since the component fails as soon as one of these two failure threshold level is exceeded. The parallel system is being subjected to different shock sets, and each shock set is associated with a defined set of components that are impacted. The parallel system fails when the last working component fails.