Reliability inferences in a $1$-out-of-$n$:G multicomponent stress-strength system with unit gamma Gompertz-$G_0$ components

This paper considers reliability inferences in a system of stress-strength $1$ outside of $n$: G when the strength systems belong to the gamma Gompertz unit distribution family (UGG). Stochastic comparisons are obtained between the survival distribution functions of this model. Additionally, some stochastic comparisons are carried out with majorized shape parameters of the unit gamma Gompertz distribution. The asymptotic and several bootstrap confidence intervals of the reliability of the stress strength are studied. In addition, the efficiency of the asymptotic and bootstrap confidence intervals is analyzed by simulation. A numerical example based on real-life data is displayed as an illustration.