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Computing the Cdf for Degrading Dynamic Systems

机译：计算Cdf以降低动态系统

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The times and frequencies of inspection, maintenance and replacement in degrading dynamic systems are difficult to determine. Mechanistic computer models are helpful but are inefficient because its complexity and the uncertainties in system characteristics and degradation rates. Probability distributions that are traditionally calculated through Monte Carlo Methods require thousands and thousands of time consuming lifetime simulations, rendering the creation of the cumulative distribution of time to failure onerous. The paper presents a novel methodology that 1) replaces the implicit mechanistic model with a simple explicit model, 2) transforms the dynamic, probabilistic, problem into a time invariant probability problem over each cycle-time, and 3), builds the cumulative distribution function (Cdf) as the summation of the incremental service-time failure probabilities over the planned service time. Error analysis suggests ways to predict and minimize errors. A Case Study of a servo-control mechanism shows how the new methodology builds a Cdf and yet provides controllable accuracy and a substantial time reduction when compared to Monte Carlo sampling with the traditional mechanistic model.
机译：难以确定降级动态系统中检查，维护和更换的时间和频率。机械计算机模型是有用的，但效率低下，因为它的复杂性以及系统特性和降级速率的不确定性。传统上通过蒙特卡洛方法计算的概率分布需要成千上万个耗时的寿命仿真，这使得创建失效时间的累积分布变得十分繁琐。本文提出了一种新颖的方法：1）用简单的显式模型代替隐式机械模型; 2）在每个周期时间内将动态，概率问题转化为时间不变概率问题; 3）建立累积分布函数（cdf）作为计划的服务时间内增量服务时间故障概率的总和。错误分析提出了预测和最小化错误的方法。伺服控制机制的案例研究表明，与传统机械模型的蒙特卡洛采样相比，新方法如何构建Cdf并提供可控制的精度和显着的时间减少。

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