Dynamic Multivariate Quantile Residual Life in Reliability Theory

Abstract EN

We extend the univariate α-quantile residual life function to multivariate setting preserving its dynamic feature.

Principal attributes of this function are derived and their relationship to the dynamic multivariate hazard rate function is discussed.

A corresponding ordering, namely, α-quantile residual life order, for random vectors of lifetimes is introduced and studied.

Based on the proposed ordering, a notion of positive dependency is presented.

Finally, a discussion about conditions characterizing the class of decreasing multivariate α-quantile residual life functions is pointed out.