{"title":"Bivariate failure modeling","authors":"Sang-Chin Yang, J. Kobza, J. A. Nachlas","doi":"10.1109/RAMS.2000.816322","DOIUrl":null,"url":null,"abstract":"Issues related to the construction of bivariate reliability models and their application to maintenance planning are discussed. The distinction between bivariate failure models and models of first passage time to a failure threshold clarifies the motivation for the development of bivariate models. The authors present a taxonomy of model classes and identify two classes as their focus. The model classes examined here are those in which the two variables are related by a stochastic function and those in which the variables are simply correlated. Examples of the models of each of the two classes are defined. The general approach to model formulation is explained so that the reader may construct alternate forms. The sometimes subtle aspects of model analysis are discussed with particular emphasis on the interpretation of bivariate failure probabilities and on the calculating of numerical results. Associated issues related to the construction of renewal models that can be used in maintenance planning are also discussed. For each of the topics addressed, example calculations are provided or else the technical roadblocks to continuing analysis are identified. In the authors' view, the types of bivariate models described here provide a new way to study the reliability of equipment for which univariate measures are incomplete. Thus, a new area of reliability research is identified. The definitions they offer may be modified, and the approach to model formulation they present may be used to define other models. They raise several open questions concerning the model construction and analysis. Both conceptual definitions and analytical methods warrant further exploration.","PeriodicalId":178321,"journal":{"name":"Annual Reliability and Maintainability Symposium. 2000 Proceedings. International Symposium on Product Quality and Integrity (Cat. No.00CH37055)","volume":"35 2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2000-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annual Reliability and Maintainability Symposium. 2000 Proceedings. International Symposium on Product Quality and Integrity (Cat. No.00CH37055)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/RAMS.2000.816322","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6

Abstract

Issues related to the construction of bivariate reliability models and their application to maintenance planning are discussed. The distinction between bivariate failure models and models of first passage time to a failure threshold clarifies the motivation for the development of bivariate models. The authors present a taxonomy of model classes and identify two classes as their focus. The model classes examined here are those in which the two variables are related by a stochastic function and those in which the variables are simply correlated. Examples of the models of each of the two classes are defined. The general approach to model formulation is explained so that the reader may construct alternate forms. The sometimes subtle aspects of model analysis are discussed with particular emphasis on the interpretation of bivariate failure probabilities and on the calculating of numerical results. Associated issues related to the construction of renewal models that can be used in maintenance planning are also discussed. For each of the topics addressed, example calculations are provided or else the technical roadblocks to continuing analysis are identified. In the authors' view, the types of bivariate models described here provide a new way to study the reliability of equipment for which univariate measures are incomplete. Thus, a new area of reliability research is identified. The definitions they offer may be modified, and the approach to model formulation they present may be used to define other models. They raise several open questions concerning the model construction and analysis. Both conceptual definitions and analytical methods warrant further exploration.
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二元失效模型
讨论了二元可靠性模型的建立及其在维修计划中的应用。二元失效模型和到达失效阈值的首次通过时间模型之间的区别阐明了二元模型发展的动机。作者提出了模型类的分类法,并确定了两个类作为他们的重点。这里检查的模型类是那些两个变量由随机函数相关的模型类和那些变量简单相关的模型类。定义了这两个类的每个模型的示例。解释了模型公式的一般方法,以便读者可以构建替代形式。讨论了模型分析的一些微妙方面,特别强调了二元失效概率的解释和数值结果的计算。本文还讨论了可用于维修计划的更新模型构建的相关问题。对于所讨论的每个主题,都提供了示例计算,或者确定了继续分析的技术障碍。在作者看来,这里描述的二元模型类型为研究单变量测量不完整的设备可靠性提供了一种新的方法。因此,确定了可靠性研究的一个新领域。它们提供的定义可以被修改,并且它们提供的模型表述方法可以用于定义其他模型。他们提出了一些关于模型构建和分析的开放性问题。概念定义和分析方法都值得进一步探索。
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