Optimizing population mean estimation under ranked set sampling with applications to Engineering

This article aims to develop two novel mean estimators of finite populations under ranked set sampling. The suggested estimators result in a high-efficiency gain due to their efficient formulation by taking the linear combination of classical estimators using optimization constants. We also discuss the theoretical properties and derive bias and mean squared error up to the first order of approximation. To theoretically validate our proposed estimators, we derive the conditions under which our estimators prevail over the competing estimators. The findings suggest that when ranked set sampling is implemented effectively, it saves cost and improves precision, serving as a potent instrument for improved decision-making, specifically in engineering applications, such as environmental monitoring, resource management, and quality control. An empirical and simulation study has been conducted using real and synthetic data to validate our methodology empirically. The suggested estimators offer a significant contribution to survey sampling in estimating mean under ranked set sampling. Further, the proposed estimator can be seamlessly adapted in other sampling designs such as simple random sampling, stratified random sampling, cluster sampling, etc, as well as in estimating other parameters such as variance, skewness, coefficient of correlation, etc. in various domains. Highlights • Objective: The objective is to formulate two novel and highly effective mean estimators for finite populations using Ranked Set Sampling (RSS). The suggested estimators are formulated by taking a linear combination of classical estimators to achieve enhanced accuracy and efficacy. • Theoretical framework: The theoretical framework examines the bias and mean square error (MSE) of the estimators and identifies the circumstances in which they are more effective than traditional methods. • Applications: This study illustrates the practicality of the estimators in engineering domains such as environmental monitoring, resource management, and quality control. • Cost-Effectiveness: Emphasis is placed on the ability of RSS to decrease expenses and enhance accuracy, thereby facilitating more informed decision-making when implemented efficiently. • Empirical Validation: The technique is validated through thorough empirical and simulation investigations using both actual and synthetic data. • Historical Context: This work is based on McIntyre's initial research conducted in 1952, as well as subsequent improvements made in RSS methodology. • Novel Contributions: This study presents innovative composite estimators achieved by optimizing linear combinations of conventional estimators. The suggested estimators can be easily adjusted to accommodate various parameter estimations and sampling approaches, thereby expanding their practicality. • Significance: The findings have significant implications for enhancing the accuracy and effectiveness of population mean estimations in diverse practical research disciplines.