Reliability modeling for systems subject to multiple dependent competing failure processes with shock loads above a certain level

Considering that products with high reliability have ability to resist small shock loads, a new reliability model is proposed for system experiencing dependent competing failure processes(DCFP) with shock loads above a certain level. Such shock loads are separated by the shock threshold, beyond which are fatal shocks causing sudden failure of systems. The remaining part between the certain level and shock threshold are general shock loads causing sudden degradation increments (SDI). Moreover, an explicit relationship between SDI and the magnitude of shock loads is established for reliability assessment. In this study, we consider two kinds of DCFP: (1) a shock process and a degradation process; (2) a shock process and multiple degradation processes. In case (1), we consider the dependence between shock process and degradation process with conditional probability. In case (2), we not only consider the dependence between shock process and degradation processes with conditional probability, but also the dependence between multiple degradation processes with Copulas. Finally, the effectiveness of proposed models is demonstrated by reliability analysis of the microengine developed by Sandia National Laboratories and an extended numerical example. Besides, sensitivity analysis is performed to assess the effects of model parameters on the system reliability.