Ordering Results on Comparisons of Lifetimes of Parallel Systems through the Majorization of Unit Gamma Gompertz-F Parameters

This study compares two parallel systems whose components are taken from the unit gamma Gompertz-F family. The comparisons are accomplished according to various stochastic orders, including the usual stochastic order, the reversed hazard rate order, and the likelihood ratio order by way of the majorization of shape parameters. For additional research, we investigate the lifetime of system components to be dependent or independent under conditions that the baseline distribution function of components is identical or non-identical. A numerical example based on real-life data is presented as an illustration.