ABSTRACT Several results based on the likelihood-ratio test have been discussed in the literature for testing the scale parameters of two exponential distributions under complete and different censored forms of data, many of which are asymptotic in nature. However, exact likelihood-ratio tests have been derived only for the case of complete and independent Type-II censored samples. In this paper, we first develop exact inference using the likelihood-ratio test based on two exponential samples under joint Type-II censoring. We then obtain the exact critical value as well as the power function by using both unrestricted and restricted maximum likelihood estimators (MLEs) in the likelihood-ratio test statistics. Based on these results, we discuss the procedure for designing an optimal life-testing experiment in this set-up. Finally, some numerical examples are presented for illustrating all the results developed here.

中文翻译：

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联合类型 II 删失指数数据的精确似然比检验

摘要 文献中已经讨论了基于似然比检验的几个结果，用于在完整和不同的删失数据形式下测试两个指数分布的尺度参数，其中许多数据本质上是渐近的。但是，仅针对完整且独立的 II 类删失样本的情况得出了精确的似然比检验。在本文中，我们首先使用基于联合 Type-II 审查下的两个指数样本的似然比检验来开发精确推理。然后，我们通过在似然比检验统计量中使用不受限制和受限制的最大似然估计量 (MLE) 来获得精确的临界值以及功效函数。基于这些结果，我们讨论了在此设置中设计最佳寿命测试实验的程序。最后，