Stochastic Comparisons for Series and Parallel Systems with Heterogeneous Power Lomax Component Lifetimes

The present communication provides a comparison between the lifetimes of the series and the parallel systems with independent heterogeneous power Lomax ( $$\mathcal{PL}$$ ) component lifetimes with respect to the usual stochastic ordering and the reversed hazard rate ordering. The sufficient conditions for the comparison of the lifetimes of two series systems have been developed when the heterogeneity is assumed in two model parameters. In addition, the reversed hazard rate ordering between the lifetimes of the parallel systems for multiple-outlier models have been established. Various examples and counterexamples have been presented to illustrate the theoretical establishments.