Reliability modelling for multi-component systems subject to stochastic deterioration and generalized cumulative shock damages

For a complex system consisting of multiple components, it is often unrealistic that one type of environmental shocks affects all the components at the same time. Correspondingly, random shocks are categorized into several distinct sets according to their functions, attributes or sizes. This study develops generalized reliability models for multi-component systems, where each component is subject to two dependent competing failure processes, i.e., a soft failure process caused jointly by internal performance degradation and an incremental damage due to effective external shock sets, and a hard failure process caused by the same random shocks. A damage improvement coefficient and a damage aggravation coefficient are respectively introduced to extend the standard cumulative shock damage model into two more generalized shock cases. Analytical representations of system reliability for a series-parallel system and a parallel-series system are derived based on a gamma to normal distribution approximation approach. To quantitatively compare the effects of these two damage coefficients, a block replacement policy is further adopted by searching for the optimal replacement intervals with a Nelder-Mead downhill simplex method. Finally, an illustrative example of micro-electro-mechanical systems (MEMS) consisting of four silicon micro-mechanical resonators is provided to examine the effects of self-healing ability in the materials of polymer binder on system reliability and replacement period.