The object of the present paper is the study of the joint lifetime of d components subject to a common stressful external environment. Out of the stressing environment, the components are independent and the lifetime of each component is characterized by its failure (hazard) rate function. The impact of the external environment is modelled through an increase in the individual failure rates of the components. The failure rate increments due to the environment increase over time and they are dependent among components. The evolution of the joint failure rate increments is modelled by a non negative multivariate additive process, which include Lévy processes and non-homogeneous compound Poisson processes, hence encompassing several models from the previous literature. A full form expression is provided for the multivariate survival function with respect to the intensity measure of a general additive process, using the construction of an additive process from a Poisson random measure (or Poisson point process). The results are next specialized to Lévy processes and other additive processes (time-scaled Lévy processes, extended Lévy processes and shock models), thus providing simple and easily computable expressions. All results are provided under the assumption that the additive process has bounded variations, but it is possible to relax this assumption by means of approximation procedures, as is shown for the last model of this paper.

本文的目的是研究d的联合寿命组件受到共同的压力外部环境。在压力环境之外，组件是独立的，每个组件的寿命由其故障（危险）率函数来表征。外部环境的影响是通过增加组件的单个故障率来模拟的。由于环境导致的故障率增加会随着时间的推移而增加，并且它们依赖于组件。联合故障率增量的演变由非负多元加法过程建模，包括 Lévy 过程和非均匀复合泊松过程，因此包含了以前文献中的几个模型。关于一般加法过程的强度测量，为多元生存函数提供了完整的形式表达式，使用从泊松随机测量（或泊松点过程）构建加法过程。结果接下来专门用于 Lévy 过程和其他加法过程（时间尺度的 Lévy 过程、扩展的 Lévy 过程和冲击模型），从而提供简单且易于计算的表达式。所有结果都是在加法过程具有有限变化的假设下提供的，但可以通过近似程序来放松这一假设，如本文最后一个模型所示。