Degradation-shock competing failure modeling considering randomness of failure threshold
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摘要:
针对大多竞争失效可靠性研究未考虑失效阈值随机性的情况，提出一种随机失效阈值影响下的竞争失效系统可靠性评价模型。分析冲击影响下退化过程中退化量及退化率的变化，并在此基础上考虑阈值随机性。讨论累积退化影响下的冲击过程，以系统所能承受的强度分布描述冲击失效阈值，并结合累积退化量的期望水平建立随时间变化的冲击失效阈值，从而明确描述了冲击失效阈值与退化过程之间的依赖关系，给出竞争失效过程的可靠性函数。以微电机系统为例进行对比及敏感性分析，验证了随机失效阈值的引入更能反映系统真实运行状态。
Abstract:Since most research on competing failure reliability do not take the unpredictability of the failure threshold into account, a competing failure reliability model that takes the randomness of the failure threshold into account is devised. The variation of degradation quantity and degradation rate under shocks was analyzed, and the randomness of the threshold was considered on this basis. The cumulative degradation under the influence of the random shock process was analyzed. The shock failure threshold is described by the strength distribution that the system can withstand, and the shock failure threshold that changes with time is established based on the expected level of cumulative degradation, so the dependence between the shock failure threshold and the degradation process is clearly described, and the reliability function of the competing failure process is given. Last but not ultimately, a micromotor system is used as a comparison and sensitivity analysis example to confirm the logic and efficacy of the suggested concept.
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图 2 考虑阈值随机性的2种竞争相依失效过程
Figure 2. Two dependent competing failure processes considering random failure threshold
图 4 随机性与退化影响的冲击失效阈值
Figure 4. Random threshold and degradation effects on hard failure threshold
图 10 不同阈值分布类型的影响分析
Figure 10. Influence analysis of different threshold distribution types
表 1 参数取值
Table 1. Parameter values
参数 数值 来源 ${\beta _0}\sim N({\mu _\beta },\sigma _\beta ^2)$ $\begin{gathered} {\mu _\beta } = 8.482\;3 \times {10^{ - 9} } \\ {\sigma _\beta } = 6.001\;6 \times {10^{ - 10} } \\ \end{gathered}$ 文献[6] $W\sim N({\mu _W},\sigma _W^2)$ $\begin{gathered} {\mu _W} = 1.2 \\ {\sigma _W} = 0.2 \\ \end{gathered} $ 文献[16] ${\mu _h}$ $1.25 \times {10^{ - 3}}$ 文献[16] $\lambda /{\rm{revolutions}}$ $2.5 \times {10^{ - 5} }$ 文献[6] $c/ ({ {\text{μm} }^3}\cdot{\text{GPa} }^{-1 })$ ${\text{8} }{\text{.333} } \times {\text{1} }{ {\text{0} }^{ - 5} }$ 文献[16] $\omega \sim W(\eta ,\gamma ,{\mu }_{\omega })$ $\begin{gathered} {\mu _\omega }{\text{ = } }0.85 \\ \eta = 0.685\;8 \\ \gamma = 1.569\;6 \\ \end{gathered}$ 假设 $\alpha $ 0 假设 $a$ $5 \times {10^{ - 6}}$ 假设 $p$ $100$ 假设 ${\sigma _\varepsilon }$ ${10^{ - 10}}$ 假设 $\sigma _h^2$ ${10^{ - 7}}$ 假设 注：revolutions表示发动机每一转。 
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