Estimation of the system reliability for generalized inverse Lindley distribution based on different sampling designs

In this paper, we are interested in estimating stress-strength reliability when the distributions of stress and strength are independent generalized inverse Lindley (GIL) under different sampling designs, namely, simple random sampling (SRS), ranked set sampling (RSS) and percentile ranked set sampling (PRSS). In the context of parameter estimation, we use maximum likelihood (ML) methodology. The performance of the ML estimators of stress-strength reliability based on SRS, RSS and PRSS are compared via a Monte-Carlo simulation study for different parameter settings and sample sizes under the assumptions of perfect and imperfect ranking, respectively. At the end of the study, the insulin resistance data set is analyzed to implement the proposed methodologies.