Research Article Reliability Estimation of Inverse Lomax Distribution Using Extreme Ranked Set Sampling Amer Ibrahim Al-Omari , 1 Amal S. Hassan, 2 Naif Alotaibi , 3 Mansour Shrahili , 4 and Heba F. Nagy 2 1 Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq 25113, Jordan 2 Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt 3 Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 11432, Saudi Arabia 4 Department of Statistics and Operations Research, King Saud University, Riyadh 11451, Saudi Arabia Correspondence should be addressed to Amer Ibrahim Al-Omari; alomari_amer@yahoo.com Received 13 September 2021; Accepted 6 November 2021; Published 22 December 2021 Academic Editor: Giorgio Kaniadakis Copyright © 2021 Amer Ibrahim Al-Omari et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In survival analysis, the two-parameter inverse Lomax distribution is an important lifetime distribution. In this study, the estimation of R = P ½Y < X is investigated when the stress and strength random variables are independent inverse Lomax distribution. Using the maximum likelihood approach, we obtain the R estimator via simple random sample (SRS), ranked set sampling (RSS), and extreme ranked set sampling (ERSS) methods. Four different estimators are developed under the ERSS framework. Two estimators are obtained when both strength and stress populations have the same set size. The two other estimators are obtained when both strength and stress distributions have dissimilar set sizes. Through a simulation experiment, the suggested estimates are compared to the corresponding under SRS. Also, the reliability estimates via ERSS method are compared to those under RSS scheme. It is found that the reliability estimate based on RSS and ERSS schemes is more efficient than the equivalent using SRS based on the same number of measured units. The reliability estimates based on RSS scheme are more appropriate than the others in most situations. For small even set size, the reliability estimate via ERSS scheme is more efficient than those under RSS and SRS. However, in a few cases, reliability estimates via ERSS method are more accurate than using RSS and SRS schemes. 1. Introduction The inverse Lomax (ILo) distribution is considered as the reciprocal of the Lomax distribution. In some situations, it is a good alternative to the famous distributions like gamma, inverse Weibull, and Weibull. It has varied applications in modelling several types of data, including economics and actuarial sciences (see [1]). It has an application in geophys- ical databases [2]. The ILo distribution has an important application in reliability analysis [3]. Statistical inference for this distribution has been discussed by several researchers (see, for example, [4, 5]). In the present work, the ILo distribu- tion is taken under the stress strength (S-S) model associated with any system that depends on different sampling schemes. The cumulative distribution function (cdf) of the ILo distribu- tion with shape parameter ω and scale parameter ρ is specified by the following: Hx ; ρ, ω ð Þ = 1+ ρ x   −ω , x, ρ, ω >0: ð1Þ The probability density function (pdf) of the ILo distribu- tion is as follows: hx ; ρ, ω ð Þ = ρω x 2 1+ ρ x   −ω−1 , x, ρ, ω >0: ð2Þ Hindawi Advances in Mathematical Physics Volume 2021, Article ID 4599872, 12 pages https://doi.org/10.1155/2021/4599872