Interval estimation of the system reliability for Weibull distribution based on ranked set sampling data

Authors : Fatma Gul AKGUL, Birdal SENOGLU, Sukru ACİTAS

Pages : 1404-1416

View : 32 | Download : 11

Publication Date : 2018-10-16

Article Type : Research Paper

Abstract :Inference for the system reliability $R$ is one of the most popular prob lems in the areas of engineering, statistics, biostatistics and etc. There fore, there exist considerable numbers of studies concerning this prob lem. Traditionally, simple random sampling insert ignore into journalissuearticles values(SRS); is used for estimat ing the system reliability. However, in recent years, ranked set sam pling insert ignore into journalissuearticles values(RSS);, cost effective and efficient alternative of SRS, is used to estimate the system reliability. In this study, we consider the interval  estimation of $R$ when both the stress and the strength are independent Weibull random variables based on RSS. We first obtain the asymp totic confidence interval insert ignore into journalissuearticles values(ACI); of $R$ by using the maximum likelihood insert ignore into journalissuearticles values(ML); methodology. The bootstrap confidence interval insert ignore into journalissuearticles values(BCI); of $R$ is  also constructed as an alternative to ACI. An extensive Monte-Carlo simulation study is conducted to compare the performances of ACI and  BCI of $R$ for different settings. Finally, a real data set is analyzed to demonstrate the implementation of the proposed methods. 
Keywords : Stress strength model, Ranked set sampling, Monte Carlo simulation, Asymptotic confidence interval, Bootstrap confidence interval