Thesis (Ph.D.) - Cairo University - ِInsitute of statistical studies and research - Department of Mathematical Statistics

Ranked set sampling approach is considered a cost efficient alternative to simple random sampling when observations are costly or time-consuming but the ranking of the observations without actual measurement can be done relatively easily. Many authors suggested different modifications for ranked set sampling to come up with new sampling techniques. Median ranked set sampling, extreme ranked set sampling and percentile ranked set sampling are some modifications for ranked set sampling. In this dissertation research, the estimation of when and are two independent Burr type XII distributions is considered. Maximum likelihood method is proposed to estimate based on ranked set sampling and some of its modifications. The research methodology adapted here is to estimate the reliability in multicomponent by using maximum likelihood method of estimation based on different types of ranked set sampling, the reliability estimators for stress strength model are obtained when samples drawn from Burr type XII distributions. Additionally, Bayesian estimator of R using squared error and linear exponential loss functions based on simple random sampling, ranked set sampling and median ranked set sampling. Numerical study is carried out to compare the different estimators

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