A BIVARIATE FAILURE TIME MODEL, WITH DEPENDENCE DUE TO SHOCKS AND MIXED EFFECT

Ha Pham (1) , Sophie Mercier (2)

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

A two-component system is considered, which is subject to external and possibly fatal shocks. The lifetimes of both components are characterized by their hazard rates. Each shock can cause the immediate failure of one single or of 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 for the joint distribution of the bivariate lifetime of the two components is provided. Some positive dependence properties of the bivariate lifetime are found out. The influence of the shock model parameters on the bivariate lifetime is studied.

Mots clés: Bivariate non-homogeneous compound Poisson process; Hazard rate process; Aging properties; Positive dependence properties

Domaines: Probabilités [math.PR]

Ha Pham, Sophie Mercier. A BIVARIATE FAILURE TIME MODEL, WITH DEPENDENCE DUE TO SHOCKS AND MIXED EFFECT. MMR 2015: Ninth International Conference on Mathematical Methods in Reliability, 2015, Tokyo, Japan. ⟨hal-01355146⟩