Reliability Estimation of Inverse Lomax Distribution Using Extreme Ranked Set Sampling

Abstract

In survival analysis, the two-parameter inverse Lomax distribution is an important lifetime distribution. In this study, the estimation of $R=P\left[Y<X\right]$ 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.