The Failure and Hazard Processes in Multivariate Reliability Systems

The component failures in a complex multi-component system are treated in the paper as a multivariate point process, and the system failure as a univariate point process derived from this. Our main concern is to extend the well-known concept of a hazard function to this general case. It is suggested that, e.g., the system failure hazard be defined as a stochastic process, viz., the compensator of the system failure counting process relative to the σ-fields describing the system's past. The connections between such a hazard process and the lifetime distribution classes of Arjas (Arjas, E. 1981. A stochastic process approach to multivariate reliability systems: Notions based on conditional stochastic order. Math. Oper. Res.6 263–276.) are also discussed.