- Hacettepe Journal of Mathematics and Statistics
- Vol: 47 Issue: 5
- Interval estimation of the system reliability for Weibull distribution based on ranked set sampling ...
Interval estimation of the system reliability for Weibull distribution based on ranked set sampling data
Authors : Fatma Gul Akgul, Birdal Senoglu, Sukru Acitas
Pages : 1404-1416
View : 17 | Download : 9
Publication Date : 2018-10-16
Article Type : Research
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 (SRS) is used for estimat ing the system reliability. However, in recent years, ranked set sam pling (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 (ACI) of $R$ by using the maximum likelihood (ML) methodology. The bootstrap confidence interval (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