Further Results on Relative Aging Orders and Comparison of Record Statistics

In reliability engineering, relative aging is an important notion useful for measuring how a system ages relative to another. In recent years, the reliability properties of record statistics used for statistical modeling, such as shock models, have been investigated. This study presents new findings regarding aging faster orders. Several implications of relative aging orders are presented, including further inequalities arising from these stochastic orders. We apply two faster aging orders by comparing distributions using their cumulative hazard rate functions and cumulative reversed hazard rate functions in the upper and lower record values, respectively. In addition, we compare the record statistics in the two-sample problem. The extent to which the aging-induced faster orders are preserved in the record statistics resulting from sequences of independent and identically distributed random lifetimes is investigated. Finally, examples are provided to illustrate these concepts.