Stress–Strength Reliability for the Generalized Inverted Exponential Distribution Using MRSS

In this paper, we study the estimation of the stress–strength reliability model when the stress and the strength variables are modeled by two independent but not identically distributed random variables from the generalized inverted exponential distributions. The stress strength reliability estimator is considered using, mainly, median ranked set sampling (MRSS) compared to ranked set sampling (RSS) and simple random sampling (SRS). Firstly, we discussed the reliability estimation when the data of the strength and stress random variables are in the form of the MRSS with even or odd set sizes. Secondly, we derived the reliability estimator when the data of the strength variable are selected using the MRSS with even or odd set sizes. In contrast, the data of the stress variable are drawn using RSS and vice versa. Thirdly, we obtained the reliability estimator when the data of the strength variable are selected using the MRSS with even or odd set sizes, while the data of the stress variable are chosen using the SRS and vice versa. Monte Carlo simulation study is performed to compare the behavior of different estimates with respect to the MRSS scheme. This study indicated that the reliability estimates based on MRSS are more efficient than the corresponding estimates based on the RSS and SRS in most of the situations. One real data analysis has been performed for illustrative purposes.