The mean past lifetime (MPL) is an important tool in reliability and survival analysis for measuring the average time elapsed since the occurrence of an event, under the condition that the event has occurred before a specific time \(t>0\). This article develops a nonparametric estimator for MPL based on observations collected according to ranked set sampling (RSS) design. It is shown that the proposed estimator is a strongly uniform consistent estimator of MPL. It is also proved that the introduced estimator tends to a Gaussian process under some mild conditions. A Monte Carlo simulation study is employed to evaluate the performance of the proposed estimator with its competitor in simple random sampling (SRS). Our findings show the introduced estimator is more efficient than its counterpart estimator in SRS as long as the quality of ranking is better than random. Finally, an illustrative example is provided to describe the potential application of the developed estimator in assessing the average time between the infection and diagnosis in HIV patients.

平均过去寿命 (MPL) 是可靠性和生存分析中的重要工具，用于在事件发生在特定时间\(t>0\)之前的条件下测量事件发生后的平均经过时间. 本文基于根据排序集抽样 (RSS) 设计收集的观察结果开发了 MPL 的非参数估计器。结果表明，所提出的估计器是 MPL 的强一致一致估计器。还证明了引入的估计量在一些温和条件下趋于高斯过程。蒙特卡罗模拟研究用于评估所提出的估计器与其竞争对手在简单随机抽样 (SRS) 中的性能。我们的研究结果表明，只要排名的质量优于随机，引入的估计器比 SRS 中的对应估计器更有效。最后，提供了一个说明性示例来描述开发的估计器在评估 HIV 患者感染和诊断之间的平均时间方面的潜在应用。