The sequential order statistics (SOSs) are usually used to modeling the lifetime of the sequential (n-r + 1)-out-of-n systems. In this article, we discuss the concept of progressive sequential order statistics (PSOS) as an extension of the SOS for providing more flexibility in analysis and design of engineering systems. The proposed model comes from a combination of progressive censoring and SOS. An explicit expression for the likelihood function of the PSOS data is derived. While the lifetimes of the components follow the Rayleigh distribution, the problem of parameters estimation is studied in a greater detail under the conditional proportional hazard rate model. An algorithm for generating PSOS data is suggested for simulation studies.

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