Stochastic comparisons of parallel and series systems with heterogeneous resilience-scaled components

Abstract

By adding a resilience parameter to the scale model, a general distribution family called resilience-scale model is introduced including exponential, Weibull, generalized exponential, exponentiated Weibull and exponentiated Lomax distributions as special cases. This paper carries out stochastic comparisons on parallel and series systems with heterogeneous resilience-scaled components. On the one hand, it is shown that more heterogeneity among the resilience-scaled components of a parallel [series] system with an Archimedean [survival] copula leads to better [worse] performance in the sense of the usual stochastic order. On the other hand, the [reversed hazard] hazard rate order is established for two series [parallel] systems consisting of independent heterogeneous resilience-scaled components. The skewness and dispersiveness are also investigated for the lifetimes of two parallel systems consisting of independent heterogeneous and homogeneous [multiple-outlier] resilience-scaled components. Numerical examples are provided to illustrate the effectiveness of our theoretical findings. These results not only generalize and extend some known ones in the literature, but also provide guidance for engineers to assemble systems with higher reliability in practical situations.