A Bi-Level Weibull Model with Applications to Two Ordered Events

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Original languageEnglish
Pages (from-to)1-9
Journal / PublicationInternational Journal of Prognostics and Health Management
Issue number2
Online published5 Aug 2017
Publication statusPublished - 2017


In this paper, we propose and study a new bivariate Weibull model, called Bi-levelWeibullModel, which arises when one failure occurs after the other. Under some specific regularity conditions, the reliability function of the second event can be above the reliability function of the first event, and is always above the reliability function of the transformed first event, which is a univariate Weibull random variable. This model is motivated by a common physical feature that arises fromseveral real applications. The two marginal distributions are a Weibull distribution and a generalized three-parameter Weibull mixture distribution. Some useful properties of the model are derived, and we also present the maximum likelihood estimation method. A real example is provided to illustrate the application of the model.