  This manuscript investigates the stochastic comparisons of the second-order
statistics from dependent and heterogeneous general semi-parametric family of
distributions observations. Some sufficient conditions on the usual stochastic
order of the second-order statistics from dependent and heterogeneous
observations are established under the p-larger order and the reciprocally
majorization order. Some numerical examples are given to illustrate the
theoretical findings. In addition, the results of the Theorem are applied to
two important models. Finally, we use a group of real data for empirical
analysis to carry out reliability analysis.
