In this paper, we investigate the skewness of order statistics stemming from multiple-outlier proportional hazard rates samples in the sense of several variability orderings such as the star order, Lorenz order and dispersive order. It is shown that the more heterogeneity among the multiple-outlier components will lead to a more skewed lifetime of ak-out-of-nsystem consisting of these components. The results established here generalize the corresponding ones in Kochar and Xu (J Appl Probab 48:271–284,2011, Ann Oper Res 212:127–138,2014). Some numerical examples are also provided to illustrate the theoretical results.
