<p>The Erlang distribution in classical statistics has traditionally been used for reliability analysis when there is no uncertainty in the underlying data. However, this classical framework cannot be applied in environments with inherent uncertainty. To address this limitation, we introduce the Erlang distribution under neutrosophic statistics, which incorporates the degree of indeterminacy into the analysis. In this paper, we present the fundamental properties of the proposed neutrosophic Erlang distribution and highlight its advantages over the classical approach. Unlike the existing algorithms based on the classical Erlang distribution, which cannot account for indeterminacy, we propose a novel algorithm to generate data from the neutrosophic Erlang distribution while considering varying degrees of indeterminacy. Furthermore, we conduct an extensive simulation study and demonstrate the application of the proposed distribution. Our findings reveal that the degree of indeterminacy significantly influences data generation in the Erlang distribution, emphasizing the need for decision-makers to carefully account for indeterminacy when utilizing this distribution.</p>