In this paper, a new sampling method is introduced by ordering
the maxima of ranked set samples with unequal sizes. In this new
modification of ranked set sampling which is called OMRSSU, the
pdf, cdf and joint pdf are obtained. Also, a new distribution-free
prediction interval for future order statistics is derived. In addition,
the moments of OMRSSU for exponential distribution are computed
and then the best linear unbiased estimators of exponential distribution
are obtained using OMRSSU. Finally, a comparison is made
between BLUE-OMRSSU and the BLUE based on ranked set sampling,
ordered ranked set sampling, maximum ranked set sampling and
order statistics from a simple random sample.