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

Shuguang Song, Hanlin Liu, Mimi Zhang, and Min Xie
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ijphm_17_011.pdf358.26 KBAugust 5, 2017 - 6:54pm

In this paper, we propose and study a new bivariate Weibull model, called Bi-level Weibull Model, 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 from several 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.

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Submission Keywords: 
Bi-level Weibull distribution
Generalized three-parameter Weibull mixture
Maximum likelihood estimation
Submission Topic Areas: 
Modeling and simulation
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