ObjectiveThis paper aims to introduce an algorithm designed for generating random variates in situations characterized by uncertainty.MethodThe paper outlines the development of two distinct algorithms for producing both minimum and maximum neutrosophic data based on the Weibull distribution.ResultsThrough comprehensive simulations, the efficacy of these algorithms has been thoroughly assessed. The paper includes tables presenting neutrosophic random data and an in-depth analysis of how uncertainty impacts these values.ConclusionThe study's findings demonstrate a noteworthy correlation between the degree of uncertainty and the neutrosophic minimum and maximum data. As uncertainty intensifies, these values exhibit a tendency to decrease.