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.
Highlights
Components are considered, which are made dependent through shocks arising from a common external environment
We provide here sufficient conditions under which Y has the Bivariate New Better than Used (BNBU) property in the following sense: FY (s1 + s2, t1 + t2) ≤ FY (s1, t1)FY (s2, t2)
We proposed here a bivariate random shock model with competing failure modes
Summary
Components are considered, which are made dependent through shocks arising from a common external environment. Except for these shocks, the components are assumed to evolve independently. The components may fail either when the shocks occur or between them. Each shock may lead to simultaneous failures, called common cause failures. There are many possible causes for such shocks. According to [15], they can be due to “interfaces, the environment, and major adverse events. The interfaces include power, cooling, material inputs, and external controls. The environment can produce excess temperature, pressure, vibration, impact, noise, and contamination.
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