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Improving tail accuracy of the predicted cumulative distribution function of time of failure

机译：提高预测失败时间累积分布函数的尾准确度

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Prognostic information is used to make decisions such as when to perform maintenance or - in time sensitive and safety critical applications - when to change operational settings. Where distributions about expected end of life (EOL) are available, these decisions are often based on risk-informed thresholds, for example a 2 sigma or 3 sigma criterion which considers the probability of making a bad decision at 5% or 0.3%, respectively, as tolerable. Sampling-based techniques such as Monte Carlo Sampling (MCS) and Latin Hypercube Sampling (LHS) can provide effective approaches to the propagation and analysis of uncertainty. Due to its efficient manner of stratifying across the range of each sampled variable, LHS requires less computational effort than MCS and is therefore more often used. However, since the focus is placed on accurately predicting the tails of the Cumulative Distribution Function (CDF) of Time of Failure (ToF) sampling-base techniques may not properly represent these areas. Although one might be tempted to use a brute force approach and simply increase the number of samples, some safety-critical applications may be computationally constrained. Such applications include electric UAV where the decision making process has to be fast in order to take action as soon as possible. This paper explores the ability of MCS and LHS to perform tail prediction with small sample sizes. The results show that LHS does not provide a significant advantage over MCS in terms of characterizing the tails of the CDF of the battery End of Discharge (EOD) prediction. Then, a methodology that combines MCS and Kernel Density Estimation (KDE) is investigated. The advantages of KDE in terms of reducing sample size while improving tail accuracy are demonstrated on battery end-of-discharge data.
机译：预后信息用于制定决策，例如何时执行维护或 - 时间敏感和安全关键应用程序 - 何时更改操作设置。如果有关于预期寿命末端（EOL）的分布，这些决定通常基于风险通知的阈值，例如2 sigma或3个Σicla标准，以分别以5％或0.3％的概率进行错误决定，可容忍。基于采样的技术，如蒙特卡罗采样（MCS）和拉丁超立方体采样（LHS）可以提供对不确定性的传播和分析的有效方法。由于其在每个采样变量的范围内分层的有效方式，LHS需要比MCS更少的计算工作，因此更常用。然而，由于重点放置在精确地预测失败时间（TOF）的累积分布函数（CDF）的尾部（TOF），因此采样基础技术可能无法正确代表这些区域。虽然可能被诱惑使用蛮力方法并简单地增加样本的数量，但是一些安全关键的应用程序可以计算得以计算限制。这些应用包括电动UAV，其中决策过程必须快速才能尽快采取行动。本文探讨了MCS和LHS对小型样本尺寸进行尾部预测的能力。结果表明，在表征放电电池端（EOD）预测的CDF的尾部，LHS在MCS上没有提供显着优势。然后，研究了结合MCS和核密度估计（KDE）的方法。在电池端放电数据上证明了KDE在降低样品尺寸的同时，KDE在提高尾部精度方面的优点。

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