A new Bell-exponential model: Properties and applications

In this paper, we propose a tractable Kumaraswamy Bell exponential (KwBE) distribution as a submodel of the Kumaraswamy Bell-G family of distributions. Several well-established properties are obtained for the KwBE distribution, such as the linear functional representation, rth moment, incomplete moment, moment generating function using Wright generalized hyper-geometric function, conditional moment and Réyni entropy. Based on the KwBE model, a group acceptance sampling plan (GASP) for the truncated life test is presented using median life as a quality index. Moreover, the essential design parameters are derived by defining the consumer risk and the test termination duration. The comparative study of GASP with ordinary sampling plan (OSP) is performed. A simulation study is performed to highlight the behavior of the estimates. On the inferential side, the associated parameters are estimated using a well-established maximum likelihood estimation method. The detailed model’s comparison analysis, graphical as well as numerical evidence to real-data applications, supports the theoretical work.

本文提出一种易处理的库马拉斯瓦米-贝尔指数（Kumaraswamy Bell exponential, KwBE）分布，将其作为库马拉斯瓦米-贝尔-G分布族（Kumaraswamy Bell-G family of distributions）的子模型。针对该KwBE分布，本文推导得到多项经典性质，涵盖线性泛函表示、r阶矩、不完全矩、基于赖特广义超几何函数（Wright generalized hyper-geometric function）的矩生成函数、条件矩以及雷尼熵（Réyni entropy）。基于该KwBE模型，本文以中位寿命作为质量指标，提出了面向截尾寿命试验的群验收抽样方案（group acceptance sampling plan, GASP）。通过定义使用方风险与试验终止时长，推导得到该方案的核心设计参数。此外，本文还开展了GASP与常规抽样方案（ordinary sampling plan, OSP）的对比研究。为探究参数估计量的表现特性，本文设计了仿真试验进行验证。在统计推断层面，本文采用成熟的极大似然估计法（maximum likelihood estimation method）对相关参数进行估计。最后，通过详细的模型对比分析，结合可视化与数值化的实际数据集应用案例，证实了本文理论工作的有效性与合理性。