In this paper, through the monotonicity property of reversed hazards ratio, a new stochastic ordering is introduced. Two well-known parametric families of distributions are proved to be ordered with respect to their parameters, according to the new proposed stochastic order. Other situations, where the new order is applicable, are described in details. A number of elementary and basic properties of the order, for example, preservation under increasing transformations are derived. Stochastic comparisons of the parallel systems are made using the new stochastic order. In parallel with the obtained results, some examples will explain the concepts.

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