Ordering results of the smallest order statistics from independent heterogeneous new modified generalized linear failure rate random variables

This article deals with stochastic comparisons of series systems comprising a new modified generalized linear failure rate family of distributions. The results are established in three directions. First, we establish based on vector majorization the usual stochastic order and the hazard rate order of series systems. Next, multiple-outlier models are considered. When the number of components is equal, the results are obtained in terms of the likelihood ratio order. For an unequal number of components, we develop comparisons according to the usual stochastic order, and hazard rate order. Then, based on weak majorization and p-larger orders between the vector of parameters, some characterization results for comparing the lifetimes of series systems are also established. Finally, we discuss based on multivariate chain majorization the usual stochastic order of series systems. Numerical examples are considered to illustrate the results.