Stochastic orders using quantile-based reliability functions

The concept of stochastic orders plays a major role in the theory and practice of statistics. It generally refers to a set of relations that may hold between a pair of distributions of random variables. In reliability theory, stochastic orders are employed to compare lifetime of two systems. In the present work, we develop new stochastic orders using the quantile-based reliability measures like the hazard quantile function and the mean residual quantile function. We also establish relationships among the proposed orders and certain existing orders. Various properties of the orders are also studied.