Multivariate stochastic orderings and positive dependence in reliability theory

Stochastic orderings are introduced for vectors of lifetimes based on hazard rates and cumulative hazard functions. Relations are established between those orderings and other ones such as the totally positive ordering of Karlin and Rinott. Positive dependence notions in reliability theory are recast in terms of the new stochastic orderings. Relationships are also established between the notion of multivariate total positivity and the notion of hazard increase upon failure.