The purpose of this study is to introduce a new T-X family lifetime distribution known as exponentiated exponential-inverse Weibull, and we refer to this distribution as EE-IW. The new model’s basic mathematical characteristics are studied. The maximum likelihood (ML) estimator (MLE) approach is used to estimate the parameters. A Monte Carlo simulation is done to examine the behavior of the estimators. Finally, a real-world dataset is utilized to show the utility of the proposed model in many industries and to compare it to well-known distributions.