In this article, we consider the problem of estimating cumulative distribution function (CDF) and a reliability parameter using moving extreme ranked set sampling (MERSS). Two different CDF estimators are described and compared with their competitors in simple random sampling (SRS) and ranked set sampling (RSS). It turns out the CDF estimators in MERSS can be more efficient than their competitors in SRS and RSS at a point in a particular tail of the distribution when the quality of rankings is sufficiently good. Motivated by this efficiency gain, we develop some estimators for the stress-strength probability using MERSS. The suggested estimators are then compared with their counterparts in the literature via Monte Carlo simulation. Finally, a real dataset is used to show the applicability of the developed procedures.

中文翻译：

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使用移动极端排名集采样及其可靠性的有效估计累积分布函数

在本文中，我们考虑使用移动极端排序集抽样（MERSS）估算累积分布函数（CDF）和可靠性参数的问题。描述了两种不同的CDF估计量，并在简单随机抽样（SRS）和排名集抽样（RSS）中将其与竞争对手进行了比较。事实证明，当排名的质量足够好时，MERSS中的CDF估算器可能会比其SRS和RSS中的竞争对手更有效。受此效率提高的激励，我们使用MERSS为应力强度概率开发了一些估计器。然后通过蒙特卡洛模拟将建议的估计量与文献中的估计量进行比较。最后，使用真实的数据集来显示所开发程序的适用性。