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Traditional k‐out‐of‐n models assume that the components are independent, while recent research studies assume that the components are dependent caused by global load‐sharing characteristic. In this paper, we investigate the consecutive k‐out‐of‐n systems with dependent components by local load‐sharing characteristic. The work load and shock load on failed components will be equally shared by adjacent components, so the components tend to fail consecutively. Consequently, the components degradation processes may be diverse, since their degradation rate (dependent on work load) and abrupt degradation (dependent on shock load) become unequal because of local load‐sharing effect. Furthermore, the system failure will be path‐dependent on the failure sequences of components, which results in that the same system states may have different system failure probabilities. This new dependence makes the system reliability model more complex. In this work, an analytical model that can be solved numerically is derived to compute the reliability with this complex dependence. The developed model is demonstrated by a cable‐strut system in the suspension bridge. The results show that the reliability decreases significantly when the new dependence is considered.

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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 microengine degrades linearly, an analytical reliability model is derived. Finally, a numerical example is conducted to illustrate the effectiveness of the developed model.