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

Abstract

Inference for the system reliability $R$ is one of the most popular problems in the areas of engineering, statistics, biostatistics and etc. Therefore, there exist considerable numbers of studies concerning this problem. Traditionally, simple random sampling (SRS) is used for estimating the system reliability. However, in recent years, ranked set sampling (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 asymptotic 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

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