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

#### Fatma Gul Akgul [1] , Birdal Senoglu [2] , Sukru Acitas [3]

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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.
Stress-strength model, Ranked set sampling, Monte-Carlo simulation, Asymptotic confidence interval, Bootstrap confidence interval
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Primary Language en Mathematics Statistics Author: Fatma Gul Akgul (Primary Author)Institution: ARTVIN ÇORUH UNIVERSITY, DEPARTMENT OF COMPUTER ENGINEERINGCountry: Turkey Author: Birdal SenogluInstitution: ANKARA UNIVERSITY, FACULTY OF SCIENCE, DEPARTMENT OF STATISTICSCountry: Turkey Author: Sukru AcitasInstitution: ANADOLU UNIVERSITY, FACULTY OF SCIENCE, DEPARTMENT OF STATISTICSCountry: Turkey
 Bibtex @research article { hujms471545, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {Hacettepe University}, year = {2018}, volume = {47}, pages = {1404 - 1416}, doi = {}, title = {Interval estimation of the system reliability for Weibull distribution based on ranked set sampling data}, key = {cite}, author = {Akgul, Fatma Gul and Senoglu, Birdal and Acitas, Sukru} } APA Akgul, F , Senoglu, B , Acitas, S . (2018). Interval estimation of the system reliability for Weibull distribution based on ranked set sampling data. Hacettepe Journal of Mathematics and Statistics, 47 (5), 1404-1416. Retrieved from http://dergipark.gov.tr/hujms/issue/39860/471545 MLA Akgul, F , Senoglu, B , Acitas, S . "Interval estimation of the system reliability for Weibull distribution based on ranked set sampling data". Hacettepe Journal of Mathematics and Statistics 47 (2018): 1404-1416 Chicago Akgul, F , Senoglu, B , Acitas, S . "Interval estimation of the system reliability for Weibull distribution based on ranked set sampling data". Hacettepe Journal of Mathematics and Statistics 47 (2018): 1404-1416 RIS TY - JOUR T1 - Interval estimation of the system reliability for Weibull distribution based on ranked set sampling data AU - Fatma Gul Akgul , Birdal Senoglu , Sukru Acitas Y1 - 2018 PY - 2018 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1404 EP - 1416 VL - 47 IS - 5 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Interval estimation of the system reliability for Weibull distribution based on ranked set sampling data %A Fatma Gul Akgul , Birdal Senoglu , Sukru Acitas %T Interval estimation of the system reliability for Weibull distribution based on ranked set sampling data %D 2018 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 47 %N 5 %R %U ISNAD Akgul, Fatma Gul , Senoglu, Birdal , Acitas, Sukru . "Interval estimation of the system reliability for Weibull distribution based on ranked set sampling data". Hacettepe Journal of Mathematics and Statistics 47 / 5 (October 2018): 1404-1416.