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.

本文提出一类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族分布的子模型。针对该KwBE分布，本文推导得到多项成熟的数理性质，涵盖线性泛函表示、r阶矩、不完全矩、基于莱特广义超几何函数的矩生成函数、条件矩以及雷尼熵。基于该KwBE模型，本文以中位寿命为质量指标，提出了一种适用于截尾寿命试验的批量验收抽样方案（group acceptance sampling plan, GASP）。此外，本文通过定义使用方风险与试验终止时长，推导出该GASP的核心设计参数。随后，本文开展了GASP与常规抽样方案（ordinary sampling plan, OSP）的对比研究。为凸显参数估计量的性能表现，本文完成了仿真模拟实验。在统计推断层面，本文采用成熟的极大似然估计法对模型关联参数进行估计。最后，通过详细的模型对比分析，以及可视化与数值化的实际数据集应用验证，佐证了本文理论工作的合理性与有效性。