Wu Zhimin, Xiang Lin
College of Data Science , Jiaxing University, Jiaxing, 314001, China.
College of Economics and Management , Zhejiang Normal University, Jinhua, 321000, China.
Sci Rep. 2025 Jul 2;15(1):22759. doi: 10.1038/s41598-025-09136-2.
Accurate system reliability estimation facilitates engineers and statisticians in optimizing resource allocation within industrial and technological applications. In the field of statistical modeling for system reliability metrics, ranked set sampling (RSS) designs have been confirmed as effective alternatives to simple random sampling (SRS). In this study, we mainly focus on investigating the performance of different sampling designs, including SRS, RSS and extreme ranked set sampling (ERSS), on estimating stress-strength reliability when stress and strength are two independent random variables following power Lindley (PL) distributions under both uncensored and right-censored data. To obtain the parameter estimates of the PL distributions, the maximum likelihood (ML) method is used. Monte Carlo simulations considering perfect and imperfect ranking with uncensored data and perfect ranking with right-censored data show that RSS and ERSS provide more precise ML estimates of system reliability, R, compared to SRS under different sample sizes and parameter settings. Finally, applications to two datasets also illustrate the advantage of our proposed methodologies, which are conducive to enhanced precision in critical systems, cost-efficient resource allocation, adaptability to real-world data challenges.
准确的系统可靠性估计有助于工程师和统计学家在工业和技术应用中优化资源分配。在系统可靠性指标的统计建模领域，排序集抽样（RSS）设计已被确认为简单随机抽样（SRS）的有效替代方法。在本研究中，我们主要关注调查不同抽样设计的性能，包括SRS、RSS和极端排序集抽样（ERSS），在应力和强度是两个独立随机变量且服从幂林德利（PL）分布的情况下，在无删失和右删失数据下估计应力-强度可靠性。为了获得PL分布的参数估计，使用了最大似然（ML）方法。考虑无删失数据的完美和不完美排序以及右删失数据的完美排序的蒙特卡罗模拟表明，与不同样本量和参数设置下的SRS相比，RSS和ERSS提供了更精确的系统可靠性R的ML估计。最后，对两个数据集的应用也说明了我们提出的方法的优势，这有利于提高关键系统的精度、实现成本效益高的资源分配以及适应实际数据挑战。
