A bivariate failure time model with random shocks and mixed effects

Sophie Mercier (1) , Ha Pham (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 Banking University of Hochiminh city

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 bivari-ate 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.

Mots clés: Positive dependence properties; Reliability; Stochastic order; Multivariate total positivity; Maximum likelihood estimator; Aging properties; Bivariate new better than used; Bivariate non-homogeneous compound Poisson process; Hazard rate order; Hazard rate process

Domaines: Probabilités [math.PR]; Statistiques [stat]

Sophie Mercier, Ha Pham. A bivariate failure time model with random shocks and mixed effects. Journal of Multivariate Analysis, 2017, 153, pp.33-51. ⟨10.1016/j.jmva.2016.09.008⟩. ⟨hal-01361399⟩