Classical statistics deals with determined and precise data analysis. But in reality, there are many cases where the information is not accurate and a degree of impreciseness, uncertainty, incompleteness, and vagueness is observed. In these situations, uncertainties can make classical statistics less accurate. That is where neutrosophic statistics steps in to improve accuracy in data analysis. In this article, we consider the Birnbaum-Saunders distribution (BSD) which is very flexible and practical for real world data modeling. By integrating the neutrosophic concept, we improve the BSD's ability to manage uncertainty effectively. In addition, we provide maximum likelihood parameter estimates. Subsequently, we illustrate the practical advantages of the neutrosophic model using two cases from the industrial and environmental fields. This paper emphasizes the significance of the neutrosophic BSD as a robust solution for modeling and analysing imprecise data, filling a crucial gap left by classical statistical methods.

翻译：经典统计学处理确定且精确的数据分析。然而现实中存在大量信息不准确、具有一定程度不精确性、不确定性、不完整性及模糊性的情况。在这些情境下，不确定性会降低经典统计分析的准确性。中智统计学正是为此而生，旨在提升数据分析的精确度。本文研究具有高度灵活性和实用性的Birnbaum-Saunders分布（BSD）用于现实世界数据建模。通过融入中智概念，我们增强了BSD有效处理不确定性的能力。此外，我们提供了参数的最大似然估计方法。随后，通过工业与环境领域的两个案例，我们展示了中智模型的实际优势。本文强调了中智BSD作为不精确数据建模与分析的有效解决方案的重要性，填补了经典统计方法遗留的关键空白。