A simple classification approach to build a bathtub

B. Haan
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引用次数: 3

Abstract

The notional bathtub curve is often cited to describe how a device's failure rate may change with age. Modeling the bathtub curve or other undulating function to capture the reliability-centric phases of life can be accomplished using the mixed-Weibull distribution. Unfortunately, fitting failure data directly to the mixed-Weibull distribution typically requires an assumption of the number of subpopulations within the distribution and difficult computations that often end in the utilization of complex algorithms. The fitting approach described in this paper provides a tactic that can perform the fit without assuming a set number of subpopulations and can be implemented in a basic spreadsheet. This paper begins with a brief examination of a common mixed-Weibull form. It is observed that the likelihood function of this form implicitly handles the data in aggregate - ironically not a mixture. This can be addressed with a modest adjustment but at the cost of greatly increasing the number of parameters that must be considered to fit the distribution. Two separate derivations of the introduced approach are outlined. The first originates within an Artificial-Life framework used for constructing reliability models. Processes within this framework are taken to a conceptual limit. Addressing computational time issues that result yields the presented approach. Because the Artificial-Life Framework tactic is still largely unproven a second derivation based on the well established k-means clustering algorithm is provided as an alternate. Because k-means clustering algorithms are well known, their behavior provides predictions into the behavior of the approach being introduced. The mechanics of the approach are outlined and detailed using sample data. One simple sample set demonstrates the mechanics while a second, more contextually rich set of data illustrates a more realistic application and behavior of the approach. In each, individual reliability data are classified and subpopulations emerge to quickly estimate parameters for a mixed-Weibull distribution. Performance characteristics are noted to be very similar to the k-means algorithm. Termination requires little iteration so even very complex mixtures can be assessed quickly. As predicted by its k-means derivation the approach is mildly chaotic so multiple trials may yield better solutions. Fortunately speed and ease of implementation accommodates for this shortcoming. Additionally, repeated application of the method on a set of data is shown to yield a discrete probabilistic estimate of the number of subpopulations contained within a dataset. The approach is found to be a convenient addition to the reliability analyst's toolbox.
构建浴缸的简单分类方法
浴盆曲线通常被用来描述设备的故障率如何随着使用年限的变化而变化。可以使用混合威布尔分布对浴盆曲线或其他波动函数进行建模,以捕获以可靠性为中心的生命阶段。不幸的是,将失效数据直接拟合到混合威布尔分布通常需要假设分布内的子种群数量,并且计算困难,通常以使用复杂的算法告终。本文描述的拟合方法提供了一种策略,可以在不假设一定数量的子种群的情况下执行拟合,并且可以在基本的电子表格中实现。本文首先简要介绍了一种常见的混合威布尔形式。可以观察到,这种形式的似然函数隐式地处理聚合数据-具有讽刺意味的是,它不是混合数据。这可以通过适度的调整来解决,但代价是大大增加了必须考虑的参数数量来拟合分布。本文概述了所介绍的方法的两个不同的推导。第一个源自用于构建可靠性模型的人工生命框架。在这个框架内的过程在概念上受到限制。解决计算时间问题,从而产生所提出的方法。由于人工生命框架策略在很大程度上仍未得到证实,因此基于已建立的k-means聚类算法的第二次推导作为替代方法提供。因为k-means聚类算法是众所周知的,它们的行为为所引入的方法的行为提供了预测。使用示例数据概述和详细介绍了该方法的机制。一个简单的示例集演示了机制,而另一个上下文更丰富的数据集则说明了该方法的更现实的应用和行为。在每一种情况下,个体可靠性数据被分类,并出现亚种群以快速估计混合威布尔分布的参数。性能特征与k-means算法非常相似。终止需要很少的迭代,因此即使非常复杂的混合物也可以快速评估。正如其k-means推导所预测的那样,该方法是轻度混沌的,因此多次试验可能会产生更好的解决方案。幸运的是,实现的速度和易用性弥补了这个缺点。此外,在一组数据上重复应用该方法可以产生数据集中包含的子种群数量的离散概率估计。该方法被认为是可靠性分析工具箱中一个方便的补充。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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