Statistical Analysis for the Unit Exponential Distribution Under Ranked Set Sampling with Applications to Engineering Data

In numerous research endeavors, cost-effective sampling is paramount, particularly when measuring the feature of interest is costly, intrusive, or requires a lot of time. Ranked set sampling (RSS) offers a valuable approach to optimize observational efficiency and enhance data collection. The two-parameter unit exponential distribution (UED) has emerged as a valuable tool for analyzing asymmetrical complex datasets. Its density function can exhibit various right-skewed and left-skewed shapes, making it well-suited for modeling a wide range of data. In this study, RSS is used to investigate the performance of ten classical estimation techniques for the UED parameters. Using a variety of accuracy criteria, the suggested RSS-based estimators’ performance was compared to that of simple random sampling (SRS) through a simulation study. Partial and overall rankings of the estimators were computed to identify the best estimate approach. As evidenced by simulation studies, the maximum likelihood and maximum product spacing methods demonstrate significant promise in accurately assessing the estimated quality of RSS and SRS, respectively. Due to its higher efficiency compared to SRS, RSS demonstrates superior performance in terms of mean squared error and other relevant metrics. Two practical implementations support our findings. The first set of data examines the performance and dependability of 20 components by focusing on their failure times. The second data explores the proportion of crude oil converted to gasoline, assessing its efficiency in the refining process. By effectively analyzing both failure time data and the proportion of crude oil data, industries can make informed decisions, improve efficiency, and optimize their operations.