In this paper, a new class of life distribution is proposed, named renewal new better than used in Laplace transform order (RNBUL). The test statistic for testing exponentiality versus (RNBUL) based on U-statistic is proposed. Pitman’s asymptotic efficiencies of the test and Pitman’s asymptotic relative efficiencies (PARE) are calculated. The percentiles of this test statistic are tabulated, and the powers of this test are estimated for some famous alternatives distributions in reliability such as Weibull, linear failure rate (LFR), and Gamma distributions. The problem regarding the right-censored data is also handled. Finally, some applications to elucidate the usefulness of the proposed test in reliability analysis are discussed.

中文翻译：

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比拉普拉斯变换顺序中使用的更好地测试更新新指数：可靠性中的应用

在本文中，提出了一类新的生命分布，称为更新新比在拉普拉斯变换阶（RNBUL）中使用的更好。提出了基于 U 统计量的检验指数对比 (RNBUL) 的检验统计量。计算测试的 Pitman 渐近效率和 Pitman 渐近相对效率 (PARE)。此检验统计量的百分位数已制成表格，并针对可靠性方面的一些著名替代分布（例如威布尔、线性故障率 (LFR) 和 Gamma 分布）估计了此检验的功效。还处理了关于右删失数据的问题。最后，讨论了阐明所提出的测试在可靠性分析中的有用性的一些应用。