A bivariate failure time model with random shocks and mixed effects

Sophie Mercier and Hai Ha Pham

Journal of Multivariate Analysis, 2017, vol. 153, issue C, 33-51

Abstract: Two components are considered, which are subject to common external and possibly fatal shocks. The lifetimes of both components are characterized by their hazard rates. Each shock can cause the immediate failure of either one or both components. Otherwise, the hazard rate of each component is increased by a non fatal shock of a random amount, with possible dependence between the simultaneous increments of the two failure rates. An explicit formula is provided for the joint distribution of the bivariate lifetime. Aging and positive dependence properties are described, thereby showing the adequacy of the model as a bivariate failure time model. The influence of the shock model parameters on the bivariate lifetime is also studied. Numerical experiments illustrate and complete the study. Moreover, an estimation procedure is suggested in a parametric framework, under a specific observation scheme.

Keywords: Aging properties; Bivariate new better than used; Bivariate non-homogeneous compound Poisson process; Hazard rate order; Hazard rate process; Maximum likelihood estimator; Multivariate total positivity; Positive dependence properties; Reliability; Stochastic order (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.jmva.2016.09.008

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