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Al-Saleh and Al-Kadiri first proposed double rank set sampling (DRSS). It seems that this ranked set sampling (RSS) modification can reduce the loss of RSS efficiency caused by ranking errors, and it is more effective than RSS and simple random sampling (SRS) to estimate the population mean. The proposed likelihood function is used to estimate the parameters of the three-Parameters Weibull distribution. Based on double ranked set sampling, extreme ranked set sampling, ranked set sampling (RSS) and simple random sampling (SRS) designs, the maximum likelihood estimator (MLE) is compared with the corresponding likelihood estimator. A simulation was carried out and the absolute relative biases, mean square error (MSE) and relative efficiency of different schemes were compared. It is found that, MSEs based SRS data has the largest MSEs comparing to RSS and its modifications schemes. This study revealed that DRSS technique has the superior over the rest of other sampling schemes. In almost all cases, DRSS has the smallest MSEs and largest efficiencies.

In this paper, the likelihood function for parameter estimation based on double ranked set sampling (DRSS) schemes is introduced. The proposed likelihood function is used for the estimation of the Weibull distribution parameters. The maximum likelihood estimators (MLEs) are investigated and compared to the corresponding ones based on simple random sampling (SRS) and ranked set sampling (RSS) schemes. A Monte Carlo simulation is conducted and the absolute relative biases, mean square errors, and efficiencies are compared for the different schemes. It is found that, the MLEs based on DRSS is more efficient than MLE using SRS and RSS for estimating the two parameters of the Weibull distribution (WD).