Reliability Analysis for Dependent Failure Processes and Dependent Failure Threshold

This paper presents reliability models for items subject to Multiple Dependent Competing Failure Process (MDCFP). Two dependent failure processes are studied: soft failures and hard failures. Soft failures are caused by continuous wear degradation and additional abrupt degradation damage due to a shock process. Hard failures are the result of instantaneous stress from the same shock process. These two failure processes are correlated or dependent in two respects. The arrival of each shock impacts both failure processes, and also the shock process affects the hard failure threshold level. When sustaining shocks, the item becomes more susceptible to hard failures. The latter has been a critical issue for many evolving complex devices, such as MEMS and stents. Two cases of dependency between the shock process and the hard failure threshold level are investigated. The first case is that the hard failure threshold value reduces to a lower level right after a run of m shocks. The second case is that the hard failure threshold value decreases to a lower level when the first shock is recorded above a pivotal value. Based on degradation and random shock modeling, the reliability models are developed for these two dependent failure processes. A preventive maintenance policy can then be developed based on the reliability analysis. The proposed model can be applied to similar systems that experience multiple dependent competing failure processes.