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Most Micro-Electro-Mechanical Systems (MEMS) experience natural degradation and random shocks simultaneously, and their failures are mainly the results of competing soft and hard failure processes. For some MEMS devices like micro-engines, considering that they have resistance against small shock loads, shocks can be categorized into three shock zones according to their magnitudes: safety zone, damage zone, and fatal zone. The fatal shocks can cause hard failure immediately, and the damage shocks can (i) increase the degradation level and (ii) reduce the hard failure threshold. In this paper, the effect (ii) is described by a dependence between the classifications of damage shocks and fatal shocks: after surviving a damage shock, the probability of a shock in fatal zone increases and in damage zone decreases. Due to the dependence, the Poisson process widely used in previous studies is unsuitable. A dependent zoned shock model is developed, where a Hindrance model, which is a special type of Markov point process, is first introduced to describe the damage shocks, and a Cox process is used to model the fatal shocks. Then, a general reliability model of micro-engines subject to degradation and dependent zoned shocks is developed. When the micro-engine degrades linearly, an analytical reliability model is derived. Finally, a numerical example is conducted to illustrate the effectiveness of the developed model.

A Reliability Model of Micro-Engines Subject to Natural Degradation and Dependent Zoned Shocks