Abstract: In engineering applications, systems in operation generally experience multiple shock-failure modes and mutually dependent competing failure process(MDCFP) because of the variability of environments, and thus it is necessary to consider the mutual influence between degradation and external shocks. On one hand, shock arrivals not only increase the degradation amount of the system, but also its degradation rate with time. On the other hand, the ability of the system to resist external shocks also decreases with the gradual degraded performance of the system. In this circumstance, the system is more vulnerable to damage due to the external shocks. Meanwhile, with the development of intelligence, more and more systems have self-healing mechanism after shock-arriving. In the existing literature, some scholars have only studied an external shock impact on the system degradation, but have not investigated a system degradation impact on the ability to resist random shocks. And few literatures have focused on a self-healing system with MDCFP. Based on the above analysis and background, therefore it is necessary to propose a novel reliability model, which is a self-healing system with mutually dependent competing failure process (DMDCFP), to calculate the system reliability more accurately. It has a certain theoretical significance and engineering value to consider this kind of model and its reliability analysis. This model in this paper not only brings some tools for describing real phenomena, but also opens a new way to research the degradation model and shock model, and is a supplement of the reliability modeling theory. What’s more, our achievements can also provide a new idea for the design of highly reliable engineering systems.
Therefore, a reliability analysis method for the self-healing system is developed by MDCFP, including soft failure and hard failure. In this model, the total degradation consists of internal natural degradation caused by wear and corrosion, and damage produced by external random shocks. Shocks increase the system degradation increment and rate, and the system’s ability to resist shocks decreases as the system gradually degrades, which is reflected in the change in the hard failure threshold. Moreover, soft failure will occur when the total deterioration reaches a pre-supposed threshold value and hard failure will occur when a single shock load exceeds the pre-supposed threshold value. So, the research work is exhibited as follows in detail. First, a new degradation model for the system with the self-healing mechanism is established by using the mutually dependent competing failure theory of shock and degradation models, in which the threshold of hard failure decreases as shocks arrive, and the self-healing effect is expressed by a nonnegative monotone decreasing function. Then, the reliability models of sudden and degradation failure under the circumstance with or without self-healing are shown respectively, and system reliability functions are given by utilizing the probability theory and stochastic processes. Furthermore, the analytical expressions in the case without self-healing are also derived and obtained. For convenience of calculations, a flow chart for calculating multiple integrals is provided and the detailed algorithm is shown by using the Monte Carlo simulation to calculate numerical solutions. However, due to the complexity of the model with the self-healing mechanism, the analytical solution of the reliability function cannot be obtained directly, so the simulation solution of the system reliability is estimated by the Monte Carlo simulation method.
Finally, an engineering example of the Micro-Electro-Mechanical System (MEMS) developed at Sandia National Laboratories is used in this paper to illustrate the proposed model and methods. The system is subject to processes of wear and shock, and its evolution process can be deemed as a degradation-threshold-shock model considering both the degradation and shock. For the sake of authenticity, the performance parameters of the MEMS are cited from those previous works extensively studied. Base on the background of the MEMS, the validity and effectiveness of the proposed reliability model are verified, and the sensitivity of the system is also analyzed. From the result, we can see that numerical solutions are consistent with simulation solutions generally when computing system reliability without self-healing. Besides, the system reliability with self-healing is more reliable than that without self-healing, which matches the reality well. By the sensitivity analysis, the system reliability is related to the initial threshold and the threshold reduction of hard failure, where the greater the threshold reduction of hard failure is, the lower the reliability is and the higher the initial threshold of hard failure is, the higher the system reliability is. What’s more, different self-healing functions or changes in parameters in self-healing function also have a great impact on the system reliability. To sum up, all of the factors affecting system failure in this paper are essential and are in accordance with the reality. The method discussed in this paper is also applicable to the reliability evaluation of other products with self-healing mechanism.

Key words: MDCFP, Monte Carlo, reliability, stochastic process, self-healing mechanism

摘要： 在工程应用中,环境的多变通常会使系统在运行过程中经历多种冲击及失效模式。并且随着智能化的发展,系统在受到冲击后具有自愈能力,因此,针对冲击会增加系统的退化量和退化率,且系统抵抗冲击的能力随着退化也会下降的现象,提出了具有相依竞争失效过程的复杂系统可靠性分析方法。首先应用冲击和退化的相依竞争失效理论,针对系统运行和自愈机制建立了新的退化模型,然后对无自愈和有自愈两种情况下的系统突发失效和退化失效过程进行建模,同时也得到了无自愈情况下的可靠度解析表达式。由于有自愈模型的复杂性,无法给出可靠度函数的解析解,但给出了Monte Carlo模拟的算法从而得到系统可靠度的模拟解。最后以微机电系统为例对提出的可靠性模型的正确性和有效性进行了验证,并进行了敏感性分析。

关键词: 相依竞争失效过程, Monte Carlo, 可靠性, 随机过程, 自愈机制