A Stochastic Process Approach to Multivariate Reliability Systems: Notions Based on Conditional Stochastic Order

The purpose of this paper is to introduce extensions of the well known notions IRF, DFR, NBU, and NWU in reliability theory. These extensions are applicable when considering complex multicomponent systems, where the components are not necessarily behaving independently and where, by continuous observation of the system, its past at any time t is known to some degree. The definitions are in terms of conditional stochastic order of the system's or its components' residual lifetimes, given the σ-field corresponding to observed past.