In this paper, we further investigate stochastic comparisons of the lifetime of parallel systems with heterogeneous independent Pareto components in term of the star order and convex order. It will be proved that the lifetime of a parallel system with heterogeneous independent components from Pareto model is always smaller than from the lifetime of another parallel system with homogeneous independent components from Pareto model in the sense of convex order. Also, under a general condition on the scale parameters, it is proved a result involving with star order.

This paper discusses stochastic comparisons of the parallel and series systems comprising multiple-outlier scale components. Under uncertain conditions on the baseline reversed hazard rate, hazard rate functions and scale parameters, the likelihood ratio, dispersive and mean residual life orders between parallel and series systems are established. We then apply the results for two exceptional cases of the multiple-outlier scale model: gamma and Pareto multiple-outlier components to illustrate the found results.

This paper discusses the hazard rate order of the fail-safe systems arising from two sets of independent multiple-outlier scale distributed components. Under certain conditions on scale parameters in the scale model and the submajorization order between the sample size vectors, the hazard rate ordering between the corresponding fail-safe systems from multiple-outlier scale random variables is established. Under certain conditions on the Archimedean copula and scale parameters, we also discuss the usual stochastic order of these systems with dependent components.

This paper deals with some stochastic comparisons of convolution of random variables comprising scale variables. Sufficient conditions are established for these convolutions' likelihood ratio ordering and hazard rate order. The results established in this paper generalize some known results in the literature. Several examples are also presented for more illustrations.