The usefulness of a new heavy-tailed distribution is studied in this article. The type-I heavy-tailed exponential (TI-HTE) distribution studied here has been suggested in the literature but has not been studied anywhere other than now. Some of its properties, together with graphical representations, were considered. The study utilized the maximum likelihood method in the estimation of the parameters. The primary goal is to create group acceptance sampling plans (GASP) using the TI-HTE model to determine whether units from a production process should be accepted or rejected. Through simulation studies and real-world examples, the importance of the TI-HTE model in identifying extreme behaviors beyond typical distributions like exponential or heavy-tailed distributions is emphasized.
