Choosing an optimal model for failure data analysis by graphical approach
Choosing an optimal model for failure data analysis by graphical approach
复制标题
DOI：
10.1016/j.ress.2013.02.004
复制
发表时间：
2013-07
期刊：
影响因子：
--
通讯作者：
Tieling Zhang;R. Dwight
中科院分区：
文献类型：
--
作者：
Tieling Zhang;R. Dwight
许多模型涉及多个威布尔分布的组合、对威布尔分布的修改或对其修改后的威布尔分布的扩展等，以模拟给定的故障数据集。将这些模型应用于给定数据集的建模，可以基于在威布尔概率纸（WPP）上绘制数据。其中，两个或两个以上的模型适合于拟合图的一个典型形状，而一个特定的模型可能适合于分析不同形状的图。因此，出现了一个问题，即如何为给定的数据集选择最优模型以及如何对数据建模。本文的动机就是要解决这个问题。本文总结了三个参数以上的威布尔相关模型的特点，包括两个或三个威布尔分布的截面模型、竞争风险模型和混合威布尔模型。本文所讨论的模型适用于对WPP上图形形状为凹形、凸形、s形或反s形的数据进行建模。然后，提出了基于拟合图形状的模型选择方法。给出了模型参数估计的主要步骤。此外，从实用的角度来看，WPP上数据图的范围明显突出。注意这一点很重要，因为忽略模型图的适用范围的模型的数学分析将在模型选择和参数估计中产生差异或大误差。
Many models involving combination of multiple Weibull distributions, modification of Weibull distribution or extension of its modified ones, etc. have been developed to model a given set of failure data. The application of these models to modeling a given data set can be based on plotting the data on Weibull probability paper (WPP). Of them, two or more models are appropriate to model one typical shape of the fitting plot, whereas a specific model may be fit for analyzing different shapes of the plots. Hence, a problem arises, that is how to choose an optimal model for a given data set and how to model the data. The motivation of this paper is to address this issue. This paper summarizes the characteristics of Weibull-related models with more than three parameters including sectional models involving two or three Weibull distributions, competing risk model and mixed Weibull model. The models as discussed in this present paper are appropriate to model the data of which the shapes of plots on WPP can be concave, convex, S-shaped or inversely S-shaped. Then, the method for model selection is proposed, which is based on the shapes of the fitting plots. The main procedure for parameter estimation of the models is described accordingly. In addition, the range of data plots on WPP is clearly highlighted from the practical point of view. To note this is important as mathematical analysis of a model with neglecting the applicable range of the model plot will incur discrepancy or big errors in model selection and parameter estimates.