  Progressive censoring scheme has received considerable attention in recent
years. In this paper we introduce a new type-II progressive censoring scheme
for two samples. It is observed that the proposed censoring scheme is
analytically more tractable than the existing joint progressive type-II
censoring scheme proposed by Rasouli and Balakrishnan \cite{RB:2010}. It has
some other advantages also. We study the statistical inference of the unknown
parameters based on the assumptions that the lifetime distribution of the
experimental units for the two samples follow exponential distribution with
different scale parameters. The maximum likelihood estimators of the unknown
parameters are obtained and their exact distributions are derived. Based on the
exact distributions of the maximum likelihood estimators exact confidence
intervals are also constructed. For comparison purposes we have used bootstrap
confidence intervals also. It is observed that the bootstrap confidence
intervals work very well and they are very easy to implement in practice. Some
simulation experiments are performed to compare the performances of the
proposed method with the existing one, and the performances of the proposed
method are quite satisfactory. One data analysis has been performed for
illustrative purposes. Finally we propose some open problems.
