The purpose of this research is to develop a maximum likelihood estimator (MLE) for lifetime performance index C_L for the parameter of mixture Rayleigh-Half Normal distribution (RHN) under progressively type-II right-censored samples under the constraint of knowing the lower specification limit (L). Additionally, we suggest an asymptotic normal distribution for the MLE for C_L in order to construct a mechanism for evaluating products’ lifespan efficiency. We have specified all the steps to carry out the test. Additionally, not only does hypothesis testing successfully assess the lifetime performance of items, but it also functions as a supplier selection criterion for the consumer. Finally, we have added two real data examples as illustration examples. These two applications are provided to demonstrate how the results can be applied.

中文翻译：

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终身绩效指标的决策

本研究的目的是在知道下限的情况下，在渐进式 II 型右删失样本下，为混合瑞利-半正态分布 (RHN) 的参数开发寿命性能指数C _L的最大似然估计器 (MLE)。规格限 ( L )。此外，我们建议C _L的 MLE 的渐近正态分布以构建产品寿命效率评价机制。我们已经指定了执行测试的所有步骤。此外，假设检验不仅可以成功评估物品的生命周期性能，而且还可以作为消费者选择供应商的标准。最后，我们添加了两个真实数据示例作为说明示例。提供这两个应用程序是为了演示如何应用结果。