Reliability Modeling of Complex Components Using Simulation

This paper is a continuation of papers presented at the 13th and 15th Probabilistic Safety Assessment and Management Conferences [1, 2]. The previous work presented discussions of modeling failure modes of complex components and the effects of censor bias. The first paper demonstrated how the typical method of treating failure modes as exponential gives optimistic predictions when predicting how improvements to subcomponents will perform. Instead of relying on traditional analytical methods, a more accurate approach is to model the failure modes as a race in time. Unfortunately, this does not give a closed-form solution and requires a more advanced solution. A simulation with pre-defined component attributes demonstrated the optimistic nature of classical techniques. Unfortunately for complex systems, the simulation routine may become very complex and difficult to implement. The second paper demonstrated the effect of censor bias when dealing with large amounts of success-only testing, and the difference between treating data as "missing" instead of censored.In the quest for closed-form solutions and simplicity, the world of reliability engineering relies on the exponential distribution. In most cases, it makes the solution closed-form and easy to solve. However, simple models may lead to incorrect results when modeling even something as simple as modeling to the failure mode or component/subassembly level. An excellent real-world example of using exponential distributions in this context is the typical automobile. No one expects a new car to have the same failure intensity as an older car. Obviously a more advanced approach is needed, and not just at the component level.This paper will use two approaches to analyze a simple system with components that have more than one failure mode. The first is a standard fault tree, and the second is a simulation. In both methods, various data assessment methods will be used to compare the results of both the data assessment method and the solution. A discussion of the results will follow.

本文为发表于第13届和第15届概率安全评估与管理会议（Probabilistic Safety Assessment and Management Conferences）的两篇会议论文[1, 2]的延续研究。此前的两项工作分别探讨了复杂组件失效模式建模以及截尾偏差（censor bias）的影响。第一篇论文阐明：将失效模式默认按指数分布建模的经典方法，在预测子组件改进后的性能时，会得到过于乐观的预测结果。相较于依赖传统解析方法，更精准的建模思路是将失效模式建模为时间竞争过程。遗憾的是，该思路无法得到闭合解，需要采用更进阶的求解方法。一项基于预定义组件属性的仿真实验，验证了经典方法的乐观性偏差。但对于复杂系统而言，这类仿真流程往往会变得极为繁琐，难以落地实施。第二篇论文则阐明：在开展大量仅成功测试时，截尾偏差会产生何种影响，以及将数据视为"缺失"而非"截尾"的处理方式之间的差异。

为追求解析解与建模简洁性，可靠性工程领域普遍采用指数分布开展建模。在多数场景下，该分布可将求解过程转化为闭合形式，便于计算。但即便仅针对失效模式、组件/子装配级别的建模，这类简单模型也可能得出错误结果。日常生活中典型的汽车便是该场景下使用指数分布建模的绝佳实例：无人会认为新车与旧车具有相同的失效率。显然，我们需要更进阶的建模方法，且该需求并非仅局限于组件级别。

本文将采用两种方法，对包含多失效模式组件的简单系统开展分析：第一种为标准故障树分析法，第二种则为仿真法。两种方法均会采用多种数据评估手段，以对比不同数据评估方法与求解结果之间的差异。文末将对研究结果展开讨论。